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|---|---|---|---|---|---|---|---|
gem-squad_v2-train-111100
|
5a81f74231013a001a334fee
|
Group_(mathematics)
|
A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups SN, the groups of permutations of N letters. For example, the symmetric group on 3 letters S3 is the group consisting of all possible orderings of the three letters ABC, i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 (or 3 factorial) elements. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group SN for a suitable integer N (Cayley's theorem). Parallel to the group of symmetries of the square above, S3 can also be interpreted as the group of symmetries of an equilateral triangle.
|
What does a finite number of elements include?
|
What does a finite number of elements include?
|
[
"What does a finite number of elements include?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111101
|
5a81f74231013a001a334fef
|
Group_(mathematics)
|
A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups SN, the groups of permutations of N letters. For example, the symmetric group on 3 letters S3 is the group consisting of all possible orderings of the three letters ABC, i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 (or 3 factorial) elements. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group SN for a suitable integer N (Cayley's theorem). Parallel to the group of symmetries of the square above, S3 can also be interpreted as the group of symmetries of an equilateral triangle.
|
What can a subgroup of a symmetric group SN can be expressed as?
|
What can a subgroup of a symmetric group SN can be expressed as?
|
[
"What can a subgroup of a symmetric group SN can be expressed as?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111102
|
5a81f74231013a001a334ff0
|
Group_(mathematics)
|
A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups SN, the groups of permutations of N letters. For example, the symmetric group on 3 letters S3 is the group consisting of all possible orderings of the three letters ABC, i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 (or 3 factorial) elements. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group SN for a suitable integer N (Cayley's theorem). Parallel to the group of symmetries of the square above, S3 can also be interpreted as the group of symmetries of an equilateral triangle.
|
What are the group of symmetries of a S3?
|
What are the group of symmetries of a S3?
|
[
"What are the group of symmetries of a S3?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111103
|
57283ac63acd2414000df75f
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What level of finality do mathematicians try to reach with math concepts?
|
What level of finality do mathematicians try to reach with math concepts?
|
[
"What level of finality do mathematicians try to reach with math concepts? "
] |
{
"text": [
"complete classification"
],
"answer_start": [
34
]
}
|
gem-squad_v2-train-111104
|
57283ac63acd2414000df760
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What area of classification leads to troublesome arithmetic?
|
What area of classification leads to troublesome arithmetic?
|
[
"What area of classification leads to troublesome arithmetic?"
] |
{
"text": [
"finite groups"
],
"answer_start": [
112
]
}
|
gem-squad_v2-train-111105
|
57283ac63acd2414000df761
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?
|
What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?
|
[
"What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?"
] |
{
"text": [
"Lagrange's theorem"
],
"answer_start": [
181
]
}
|
gem-squad_v2-train-111106
|
57283ac63acd2414000df762
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What can be used to classify small groups even though there is no classification of all finite groups?
|
What can be used to classify small groups even though there is no classification of all finite groups?
|
[
"What can be used to classify small groups even though there is no classification of all finite groups?"
] |
{
"text": [
"Computer algebra systems"
],
"answer_start": [
447
]
}
|
gem-squad_v2-train-111107
|
57283ac63acd2414000df763
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What describes finite simple groups as the building pieces for all finite groups?
|
What describes finite simple groups as the building pieces for all finite groups?
|
[
"What describes finite simple groups as the building pieces for all finite groups?"
] |
{
"text": [
"The Jordan–Hölder theorem"
],
"answer_start": [
748
]
}
|
gem-squad_v2-train-111108
|
5a81fab831013a001a335037
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
Both p2 and p3 are what?
|
Both p2 and p3 are what?
|
[
"Both p2 and p3 are what?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111109
|
5a81fab831013a001a335038
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What is used to classify all finite groups?
|
What is used to classify all finite groups?
|
[
"What is used to classify all finite groups?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111110
|
5a81fab831013a001a335039
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
When was the Jordan-Holder theorem published?
|
When was the Jordan-Holder theorem published?
|
[
"When was the Jordan-Holder theorem published?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111111
|
5a81fab831013a001a33503a
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What did Richard Borcherd make a complete classification of?
|
What did Richard Borcherd make a complete classification of?
|
[
"What did Richard Borcherd make a complete classification of?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111112
|
5a81fab831013a001a33503b
|
Group_(mathematics)
|
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
|
What theorem details the link between the largest finite group and modular functions?
|
What theorem details the link between the largest finite group and modular functions?
|
[
"What theorem details the link between the largest finite group and modular functions?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111113
|
57283bec2ca10214002da13c
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What group operations must occur for group law and topology to integrate well?
|
What group operations must occur for group law and topology to integrate well?
|
[
"What group operations must occur for group law and topology to integrate well?"
] |
{
"text": [
"continuous functions"
],
"answer_start": [
150
]
}
|
gem-squad_v2-train-111114
|
57283bec2ca10214002da13d
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What is the most simple example of topological groups?
|
What is the most simple example of topological groups?
|
[
"What is the most simple example of topological groups?"
] |
{
"text": [
"reals R under addition, (R ∖ {0}, ·),"
],
"answer_start": [
391
]
}
|
gem-squad_v2-train-111115
|
57283bec2ca10214002da13e
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What variables do locally compact groups share that can be studied by harmonic analysis?
|
What variables do locally compact groups share that can be studied by harmonic analysis?
|
[
"What variables do locally compact groups share that can be studied by harmonic analysis?"
] |
{
"text": [
"Haar measures"
],
"answer_start": [
577
]
}
|
gem-squad_v2-train-111116
|
5a81fbf231013a001a335041
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What allows group law and group operations to interweave?
|
What allows group law and group operations to interweave?
|
[
"What allows group law and group operations to interweave?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111117
|
5a81fbf231013a001a335042
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What is group law endowed with?
|
What is group law endowed with?
|
[
"What is group law endowed with?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111118
|
5a81fbf231013a001a335043
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What are harmonic analyses studied using?
|
What are harmonic analyses studied using?
|
[
"What are harmonic analyses studied using?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111119
|
5a81fbf231013a001a335044
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
What are topological spaces categorized by?
|
What are topological spaces categorized by?
|
[
"What are topological spaces categorized by?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111120
|
5a81fbf231013a001a335045
|
Group_(mathematics)
|
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R ∖ {0}, ·), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
|
How are groups that are not locally compact studied?
|
How are groups that are not locally compact studied?
|
[
"How are groups that are not locally compact studied?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111121
|
57283d5cff5b5019007d9fb4
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What concepts are fundamental to number theory?
|
What concepts are fundamental to number theory?
|
[
"What concepts are fundamental to number theory?"
] |
{
"text": [
"adele rings and adelic algebraic groups"
],
"answer_start": [
82
]
}
|
gem-squad_v2-train-111122
|
57283d5cff5b5019007d9fb5
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What group uses infinite field extensions with topology?
|
What group uses infinite field extensions with topology?
|
[
"What group uses infinite field extensions with topology?"
] |
{
"text": [
"the absolute Galois group"
],
"answer_start": [
208
]
}
|
gem-squad_v2-train-111123
|
57283d5cff5b5019007d9fb6
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What is used to generalize the connection of fields and groups to infinite field extensions?
|
What is used to generalize the connection of fields and groups to infinite field extensions?
|
[
"What is used to generalize the connection of fields and groups to infinite field extensions?"
] |
{
"text": [
"Krull topology"
],
"answer_start": [
286
]
}
|
gem-squad_v2-train-111124
|
57283d5cff5b5019007d9fb7
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What group is an advanced observation of infinite field extensions and groups that is adapted for the needs of algebraic geometry?
|
What group is an advanced observation of infinite field extensions and groups that is adapted for the needs of algebraic geometry?
|
[
"What group is an advanced observation of infinite field extensions and groups that is adapted for the needs of algebraic geometry?"
] |
{
"text": [
"the étale fundamental group"
],
"answer_start": [
510
]
}
|
gem-squad_v2-train-111125
|
5a81fdc831013a001a33505f
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What is basic to adele rings?
|
What is basic to adele rings?
|
[
"What is basic to adele rings?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111126
|
5a81fdc831013a001a335060
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
Which Galois group does not use topology?
|
Which Galois group does not use topology?
|
[
"Which Galois group does not use topology?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111127
|
5a81fdc831013a001a335061
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What form of topology do Matrix groups use?
|
What form of topology do Matrix groups use?
|
[
"What form of topology do Matrix groups use?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111128
|
5a81fdc831013a001a335062
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
The Galois group is adapted to the needs of what form of geometry?
|
The Galois group is adapted to the needs of what form of geometry?
|
[
"The Galois group is adapted to the needs of what form of geometry?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111129
|
5a81fdc831013a001a335063
|
Group_(mathematics)
|
for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group.
|
What is algebraic geometry adapted to the needs of?
|
What is algebraic geometry adapted to the needs of?
|
[
"What is algebraic geometry adapted to the needs of?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111130
|
57283e51ff5b5019007d9fd8
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What concept is of basic importance in modern physics?
|
What concept is of basic importance in modern physics?
|
[
"What concept is of basic importance in modern physics?"
] |
{
"text": [
"Lie groups"
],
"answer_start": [
0
]
}
|
gem-squad_v2-train-111131
|
57283e51ff5b5019007d9fd9
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What connects continuous symmetries to conserved quantities?
|
What connects continuous symmetries to conserved quantities?
|
[
"What connects continuous symmetries to conserved quantities?"
] |
{
"text": [
"Noether's theorem"
],
"answer_start": [
60
]
}
|
gem-squad_v2-train-111132
|
57283e51ff5b5019007d9fda
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What term describes the basic symmetries of the laws of mechanics?
|
What term describes the basic symmetries of the laws of mechanics?
|
[
"What term describes the basic symmetries of the laws of mechanics?"
] |
{
"text": [
"Rotation"
],
"answer_start": [
131
]
}
|
gem-squad_v2-train-111133
|
57283e51ff5b5019007d9fdb
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What concept relates measurements of time and velocity of two observers in motion relative to each other?
|
What concept relates measurements of time and velocity of two observers in motion relative to each other?
|
[
"What concept relates measurements of time and velocity of two observers in motion relative to each other?"
] |
{
"text": [
"Lorentz transformations"
],
"answer_start": [
483
]
}
|
gem-squad_v2-train-111134
|
57283e51ff5b5019007d9fdc
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What describe the complete symmetry group of Minkowski space including translations?
|
What describe the complete symmetry group of Minkowski space including translations?
|
[
"What describe the complete symmetry group of Minkowski space including translations?"
] |
{
"text": [
"Poincaré group"
],
"answer_start": [
937
]
}
|
gem-squad_v2-train-111135
|
5a81feb231013a001a33507b
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What is important to Lie groups?
|
What is important to Lie groups?
|
[
"What is important to Lie groups?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111136
|
5a81feb231013a001a33507c
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What connects Lie groups with conserved quantities?
|
What connects Lie groups with conserved quantities?
|
[
"What connects Lie groups with conserved quantities?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111137
|
5a81feb231013a001a33507d
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What are basic laws of mechanics?
|
What are basic laws of mechanics?
|
[
"What are basic laws of mechanics?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111138
|
5a81feb231013a001a33507e
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What measures the time and velocity of two observers?
|
What measures the time and velocity of two observers?
|
[
"What measures the time and velocity of two observers?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111139
|
5a81feb231013a001a33507f
|
Group_(mathematics)
|
Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
|
What are the translations in a group of Minkowski space called?
|
What are the translations in a group of Minkowski space called?
|
[
"What are the translations in a group of Minkowski space called?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111140
|
57283f6d2ca10214002da17a
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What product is created if the requirement that every element has an inverse is eliminated?
|
What product is created if the requirement that every element has an inverse is eliminated?
|
[
"What product is created if the requirement that every element has an inverse is eliminated?"
] |
{
"text": [
"monoid"
],
"answer_start": [
233
]
}
|
gem-squad_v2-train-111141
|
57283f6d2ca10214002da17b
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What type of numbers under addition form a monoid?
|
What type of numbers under addition form a monoid?
|
[
"What type of numbers under addition form a monoid?"
] |
{
"text": [
"natural numbers N (including 0)"
],
"answer_start": [
245
]
}
|
gem-squad_v2-train-111142
|
57283f6d2ca10214002da17c
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What method formally adds inverses to elements to any monoid?
|
What method formally adds inverses to elements to any monoid?
|
[
"What method formally adds inverses to elements to any monoid?"
] |
{
"text": [
"the Grothendieck group"
],
"answer_start": [
541
]
}
|
gem-squad_v2-train-111143
|
57283f6d2ca10214002da17d
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What can be replaced to simplify abstract algebra concepts?
|
What can be replaced to simplify abstract algebra concepts?
|
[
"What can be replaced to simplify abstract algebra concepts?"
] |
{
"text": [
"the binary operation"
],
"answer_start": [
896
]
}
|
gem-squad_v2-train-111144
|
5a81ff7e31013a001a33508d
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
Axioms are defined by relaxing what?
|
Axioms are defined by relaxing what?
|
[
"Axioms are defined by relaxing what?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111145
|
5a81ff7e31013a001a33508e
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What is the inverse of every element called?
|
What is the inverse of every element called?
|
[
"What is the inverse of every element called?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111146
|
5a81ff7e31013a001a33508f
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What is derived from (Q \ [0],-)?
|
What is derived from (Q \ [0],-)?
|
[
"What is derived from (Q \\ [0],-)?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111147
|
5a81ff7e31013a001a335090
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What needs to be defined in Groupoids for a and b?
|
What needs to be defined in Groupoids for a and b?
|
[
"What needs to be defined in Groupoids for a and b?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111148
|
5a81ff7e31013a001a335091
|
Group_(mathematics)
|
In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z ∖ {0}, ·), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group. Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
|
What does generalizing an n-ary group give rise to?
|
What does generalizing an n-ary group give rise to?
|
[
"What does generalizing an n-ary group give rise to?"
] |
{
"text": [],
"answer_start": []
}
|
gem-squad_v2-train-111149
|
57318c85a5e9cc1400cdc03b
|
Religion_in_ancient_Rome
|
The priesthoods of public religion were held by members of the elite classes. There was no principle analogous to separation of church and state in ancient Rome. During the Roman Republic (509–27 BC), the same men who were elected public officials might also serve as augurs and pontiffs. Priests married, raised families, and led politically active lives. Julius Caesar became pontifex maximus before he was elected consul. The augurs read the will of the gods and supervised the marking of boundaries as a reflection of universal order, thus sanctioning Roman expansionism as a matter of divine destiny. The Roman triumph was at its core a religious procession in which the victorious general displayed his piety and his willingness to serve the public good by dedicating a portion of his spoils to the gods, especially Jupiter, who embodied just rule. As a result of the Punic Wars (264–146 BC), when Rome struggled to establish itself as a dominant power, many new temples were built by magistrates in fulfillment of a vow to a deity for assuring their military success.
|
The members of what class were priests in ancient Rome?
|
The members of what class were priests in ancient Rome?
|
[
"The members of what class were priests in ancient Rome?"
] |
{
"text": [
"elite"
],
"answer_start": [
63
]
}
|
gem-squad_v2-train-111150
|
57318c85a5e9cc1400cdc03c
|
Religion_in_ancient_Rome
|
The priesthoods of public religion were held by members of the elite classes. There was no principle analogous to separation of church and state in ancient Rome. During the Roman Republic (509–27 BC), the same men who were elected public officials might also serve as augurs and pontiffs. Priests married, raised families, and led politically active lives. Julius Caesar became pontifex maximus before he was elected consul. The augurs read the will of the gods and supervised the marking of boundaries as a reflection of universal order, thus sanctioning Roman expansionism as a matter of divine destiny. The Roman triumph was at its core a religious procession in which the victorious general displayed his piety and his willingness to serve the public good by dedicating a portion of his spoils to the gods, especially Jupiter, who embodied just rule. As a result of the Punic Wars (264–146 BC), when Rome struggled to establish itself as a dominant power, many new temples were built by magistrates in fulfillment of a vow to a deity for assuring their military success.
|
What kind of political separation did not exist in Rome?
|
What kind of political separation did not exist in Rome?
|
[
"What kind of political separation did not exist in Rome? "
] |
{
"text": [
"church and state"
],
"answer_start": [
128
]
}
|
gem-squad_v2-train-111151
|
57318c85a5e9cc1400cdc03d
|
Religion_in_ancient_Rome
|
The priesthoods of public religion were held by members of the elite classes. There was no principle analogous to separation of church and state in ancient Rome. During the Roman Republic (509–27 BC), the same men who were elected public officials might also serve as augurs and pontiffs. Priests married, raised families, and led politically active lives. Julius Caesar became pontifex maximus before he was elected consul. The augurs read the will of the gods and supervised the marking of boundaries as a reflection of universal order, thus sanctioning Roman expansionism as a matter of divine destiny. The Roman triumph was at its core a religious procession in which the victorious general displayed his piety and his willingness to serve the public good by dedicating a portion of his spoils to the gods, especially Jupiter, who embodied just rule. As a result of the Punic Wars (264–146 BC), when Rome struggled to establish itself as a dominant power, many new temples were built by magistrates in fulfillment of a vow to a deity for assuring their military success.
|
What was the time span of the Roman Republic?
|
What was the time span of the Roman Republic?
|
[
"What was the time span of the Roman Republic?"
] |
{
"text": [
"509–27 BC"
],
"answer_start": [
189
]
}
|
gem-squad_v2-train-111152
|
57318c85a5e9cc1400cdc03e
|
Religion_in_ancient_Rome
|
The priesthoods of public religion were held by members of the elite classes. There was no principle analogous to separation of church and state in ancient Rome. During the Roman Republic (509–27 BC), the same men who were elected public officials might also serve as augurs and pontiffs. Priests married, raised families, and led politically active lives. Julius Caesar became pontifex maximus before he was elected consul. The augurs read the will of the gods and supervised the marking of boundaries as a reflection of universal order, thus sanctioning Roman expansionism as a matter of divine destiny. The Roman triumph was at its core a religious procession in which the victorious general displayed his piety and his willingness to serve the public good by dedicating a portion of his spoils to the gods, especially Jupiter, who embodied just rule. As a result of the Punic Wars (264–146 BC), when Rome struggled to establish itself as a dominant power, many new temples were built by magistrates in fulfillment of a vow to a deity for assuring their military success.
|
Which God exemplified just rule for the Romans?
|
Which God exemplified just rule for the Romans?
|
[
"Which God exemplified just rule for the Romans?"
] |
{
"text": [
"Jupiter"
],
"answer_start": [
822
]
}
|
gem-squad_v2-train-111153
|
57318c85a5e9cc1400cdc03f
|
Religion_in_ancient_Rome
|
The priesthoods of public religion were held by members of the elite classes. There was no principle analogous to separation of church and state in ancient Rome. During the Roman Republic (509–27 BC), the same men who were elected public officials might also serve as augurs and pontiffs. Priests married, raised families, and led politically active lives. Julius Caesar became pontifex maximus before he was elected consul. The augurs read the will of the gods and supervised the marking of boundaries as a reflection of universal order, thus sanctioning Roman expansionism as a matter of divine destiny. The Roman triumph was at its core a religious procession in which the victorious general displayed his piety and his willingness to serve the public good by dedicating a portion of his spoils to the gods, especially Jupiter, who embodied just rule. As a result of the Punic Wars (264–146 BC), when Rome struggled to establish itself as a dominant power, many new temples were built by magistrates in fulfillment of a vow to a deity for assuring their military success.
|
As a result of what war were many new temples built by victorious generals?
|
As a result of what war were many new temples built by victorious generals?
|
[
"As a result of what war were many new temples built by victorious generals?"
] |
{
"text": [
"Punic Wars"
],
"answer_start": [
874
]
}
|
gem-squad_v2-train-111154
|
57318f2c05b4da19006bd2ac
|
Religion_in_ancient_Rome
|
Roman religion was thus practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. Even the most skeptical among Rome's intellectual elite such as Cicero, who was an augur, saw religion as a source of social order. For ordinary Romans, religion was a part of daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances. Women, slaves, and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestals, who tended Rome's sacred hearth for centuries, until disbanded under Christian domination.
|
What characteristics were not inherent in Roman religious practice?
|
What characteristics were not inherent in Roman religious practice?
|
[
"What characteristics were not inherent in Roman religious practice?"
] |
{
"text": [
"faith or dogma"
],
"answer_start": [
215
]
}
|
gem-squad_v2-train-111155
|
57318f2c05b4da19006bd2ad
|
Religion_in_ancient_Rome
|
Roman religion was thus practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. Even the most skeptical among Rome's intellectual elite such as Cicero, who was an augur, saw religion as a source of social order. For ordinary Romans, religion was a part of daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances. Women, slaves, and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestals, who tended Rome's sacred hearth for centuries, until disbanded under Christian domination.
|
What was brought forth by religion in Rome?
|
What was brought forth by religion in Rome?
|
[
"What was brought forth by religion in Rome?"
] |
{
"text": [
"social order"
],
"answer_start": [
468
]
}
|
gem-squad_v2-train-111156
|
57318f2c05b4da19006bd2ae
|
Religion_in_ancient_Rome
|
Roman religion was thus practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. Even the most skeptical among Rome's intellectual elite such as Cicero, who was an augur, saw religion as a source of social order. For ordinary Romans, religion was a part of daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances. Women, slaves, and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestals, who tended Rome's sacred hearth for centuries, until disbanded under Christian domination.
|
What religious feature did each Roman home have?
|
What religious feature did each Roman home have?
|
[
"What religious feature did each Roman home have?"
] |
{
"text": [
"household shrine"
],
"answer_start": [
554
]
}
|
gem-squad_v2-train-111157
|
57318f2c05b4da19006bd2af
|
Religion_in_ancient_Rome
|
Roman religion was thus practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. Even the most skeptical among Rome's intellectual elite such as Cicero, who was an augur, saw religion as a source of social order. For ordinary Romans, religion was a part of daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances. Women, slaves, and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestals, who tended Rome's sacred hearth for centuries, until disbanded under Christian domination.
|
What type of celebrations made up the Roman calendar?
|
What type of celebrations made up the Roman calendar?
|
[
"What type of celebrations made up the Roman calendar?"
] |
{
"text": [
"religious observances"
],
"answer_start": [
773
]
}
|
gem-squad_v2-train-111158
|
57318f2c05b4da19006bd2b0
|
Religion_in_ancient_Rome
|
Roman religion was thus practical and contractual, based on the principle of do ut des, "I give that you might give." Religion depended on knowledge and the correct practice of prayer, ritual, and sacrifice, not on faith or dogma, although Latin literature preserves learned speculation on the nature of the divine and its relation to human affairs. Even the most skeptical among Rome's intellectual elite such as Cicero, who was an augur, saw religion as a source of social order. For ordinary Romans, religion was a part of daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances. Women, slaves, and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestals, who tended Rome's sacred hearth for centuries, until disbanded under Christian domination.
|
What religious group was in charge of Rome's sacred flame?
|
What religious group was in charge of Rome's sacred flame?
|
[
"What religious group was in charge of Rome's sacred flame?"
] |
{
"text": [
"Vestals"
],
"answer_start": [
1015
]
}
|
gem-squad_v2-train-111159
|
5731906a497a88190024903f
|
Religion_in_ancient_Rome
|
The Romans are known for the great number of deities they honored, a capacity that earned the mockery of early Christian polemicists. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks (interpretatio graeca), adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury.
|
How deities did the Romans have?
|
How deities did the Romans have?
|
[
"How deities did the Romans have?"
] |
{
"text": [
"great number"
],
"answer_start": [
29
]
}
|
gem-squad_v2-train-111160
|
5731906a497a881900249040
|
Religion_in_ancient_Rome
|
The Romans are known for the great number of deities they honored, a capacity that earned the mockery of early Christian polemicists. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks (interpretatio graeca), adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury.
|
What group was an influence to Roman culture?
|
What group was an influence to Roman culture?
|
[
"What group was an influence to Roman culture?"
] |
{
"text": [
"Greeks"
],
"answer_start": [
150
]
}
|
gem-squad_v2-train-111161
|
5731906a497a881900249041
|
Religion_in_ancient_Rome
|
The Romans are known for the great number of deities they honored, a capacity that earned the mockery of early Christian polemicists. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks (interpretatio graeca), adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury.
|
What sort of practices did the Greeks offer to Rome's culture?
|
What sort of practices did the Greeks offer to Rome's culture?
|
[
"What sort of practices did the Greeks offer to Rome's culture?"
] |
{
"text": [
"religious"
],
"answer_start": [
269
]
}
|
gem-squad_v2-train-111162
|
5731906a497a881900249042
|
Religion_in_ancient_Rome
|
The Romans are known for the great number of deities they honored, a capacity that earned the mockery of early Christian polemicists. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks (interpretatio graeca), adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury.
|
What myths did the Romans adapt to their needs?
|
What myths did the Romans adapt to their needs?
|
[
"What myths did the Romans adapt to their needs?"
] |
{
"text": [
"Greek"
],
"answer_start": [
457
]
}
|
gem-squad_v2-train-111163
|
5731906a497a881900249043
|
Religion_in_ancient_Rome
|
The Romans are known for the great number of deities they honored, a capacity that earned the mockery of early Christian polemicists. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks (interpretatio graeca), adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury.
|
What religion influenced augury for the Romans?
|
What religion influenced augury for the Romans?
|
[
"What religion influenced augury for the Romans?"
] |
{
"text": [
"Etruscan"
],
"answer_start": [
521
]
}
|
gem-squad_v2-train-111164
|
57319240a5e9cc1400cdc0d5
|
Religion_in_ancient_Rome
|
Imported mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiratorial (coniuratio), or subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity, as with the senate's efforts to restrict the Bacchanals in 186 BC.
|
What was the practice of religion to the Romans?
|
What was the practice of religion to the Romans?
|
[
"What was the practice of religion to the Romans?"
] |
{
"text": [
"personal choice"
],
"answer_start": [
97
]
}
|
gem-squad_v2-train-111165
|
57319240a5e9cc1400cdc0d6
|
Religion_in_ancient_Rome
|
Imported mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiratorial (coniuratio), or subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity, as with the senate's efforts to restrict the Bacchanals in 186 BC.
|
What was the standard practice in Roman religious life?
|
What was the standard practice in Roman religious life?
|
[
"What was the standard practice in Roman religious life?"
] |
{
"text": [
"public religion"
],
"answer_start": [
209
]
}
|
gem-squad_v2-train-111166
|
57319240a5e9cc1400cdc0d7
|
Religion_in_ancient_Rome
|
Imported mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiratorial (coniuratio), or subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity, as with the senate's efforts to restrict the Bacchanals in 186 BC.
|
What part of Roman religious practice involved secrecy?
|
What part of Roman religious practice involved secrecy?
|
[
"What part of Roman religious practice involved secrecy?"
] |
{
"text": [
"mysteries"
],
"answer_start": [
230
]
}
|
gem-squad_v2-train-111167
|
57319240a5e9cc1400cdc0d8
|
Religion_in_ancient_Rome
|
Imported mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiratorial (coniuratio), or subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity, as with the senate's efforts to restrict the Bacchanals in 186 BC.
|
What group viewed the mysteries as suspicious or subversive?
|
What group viewed the mysteries as suspicious or subversive?
|
[
"What group viewed the mysteries as suspicious or subversive?"
] |
{
"text": [
"conservative Romans"
],
"answer_start": [
304
]
}
|
gem-squad_v2-train-111168
|
57319240a5e9cc1400cdc0d9
|
Religion_in_ancient_Rome
|
Imported mystery religions, which offered initiates salvation in the afterlife, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiratorial (coniuratio), or subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional morality and unity, as with the senate's efforts to restrict the Bacchanals in 186 BC.
|
What did the mysteries seem to threaten that made the Romans occasionally attempt to ban them?
|
What did the mysteries seem to threaten that made the Romans occasionally attempt to ban them?
|
[
"What did the mysteries seem to threaten that made the Romans occasionally attempt to ban them?"
] |
{
"text": [
"morality and unity"
],
"answer_start": [
538
]
}
|
gem-squad_v2-train-111169
|
573193f005b4da19006bd2e4
|
Religion_in_ancient_Rome
|
As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability. One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces, among them Cybele, Isis, Epona, and gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict. For example, religious disputes helped cause the First Jewish–Roman War and the Bar Kokhba revolt.
|
What did the Romans tend to do with local religions and deities in conquered areas?
|
What did the Romans tend to do with local religions and deities in conquered areas?
|
[
"What did the Romans tend to do with local religions and deities in conquered areas? "
] |
{
"text": [
"absorb"
],
"answer_start": [
106
]
}
|
gem-squad_v2-train-111170
|
573193f005b4da19006bd2e5
|
Religion_in_ancient_Rome
|
As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability. One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces, among them Cybele, Isis, Epona, and gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict. For example, religious disputes helped cause the First Jewish–Roman War and the Bar Kokhba revolt.
|
To the Romans what did them think promoted social stability?
|
To the Romans what did them think promoted social stability?
|
[
"To the Romans what did them think promoted social stability?"
] |
{
"text": [
"preserving tradition"
],
"answer_start": [
212
]
}
|
gem-squad_v2-train-111171
|
573193f005b4da19006bd2e6
|
Religion_in_ancient_Rome
|
As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability. One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces, among them Cybele, Isis, Epona, and gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict. For example, religious disputes helped cause the First Jewish–Roman War and the Bar Kokhba revolt.
|
What facet of a foreign people did Rome add to itself to promote order?
|
What facet of a foreign people did Rome add to itself to promote order?
|
[
"What facet of a foreign people did Rome add to itself to promote order?"
] |
{
"text": [
"religious heritage"
],
"answer_start": [
331
]
}
|
gem-squad_v2-train-111172
|
573193f005b4da19006bd2e7
|
Religion_in_ancient_Rome
|
As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability. One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces, among them Cybele, Isis, Epona, and gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict. For example, religious disputes helped cause the First Jewish–Roman War and the Bar Kokhba revolt.
|
To what areas of the Roman empire did the Romans take their deities?
|
To what areas of the Roman empire did the Romans take their deities?
|
[
"To what areas of the Roman empire did the Romans take their deities?"
] |
{
"text": [
"remote provinces"
],
"answer_start": [
721
]
}
|
gem-squad_v2-train-111173
|
573193f005b4da19006bd2e8
|
Religion_in_ancient_Rome
|
As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability. One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces, among them Cybele, Isis, Epona, and gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one god or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic systems. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict. For example, religious disputes helped cause the First Jewish–Roman War and the Bar Kokhba revolt.
|
What facet of religion was not an issue for Roman?
|
What facet of religion was not an issue for Roman?
|
[
"What facet of religion was not an issue for Roman?"
] |
{
"text": [
"tolerance"
],
"answer_start": [
956
]
}
|
gem-squad_v2-train-111174
|
573195dbe6313a140071d0e0
|
Religion_in_ancient_Rome
|
In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. Augustus, the first Roman emperor, justified the novelty of one-man rule with a vast program of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Imperial cult became one of the major ways in which Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Rejection of the state religion was tantamount to treason. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.
|
After the Republic collapsed, what addition was made to the religions of Rome?
|
After the Republic collapsed, what addition was made to the religions of Rome?
|
[
"After the Republic collapsed, what addition was made to the religions of Rome?"
] |
{
"text": [
"emperors"
],
"answer_start": [
100
]
}
|
gem-squad_v2-train-111175
|
573195dbe6313a140071d0e1
|
Religion_in_ancient_Rome
|
In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. Augustus, the first Roman emperor, justified the novelty of one-man rule with a vast program of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Imperial cult became one of the major ways in which Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Rejection of the state religion was tantamount to treason. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.
|
Who was the first Roman emperor?
|
Who was the first Roman emperor?
|
[
"Who was the first Roman emperor?"
] |
{
"text": [
"Augustus"
],
"answer_start": [
110
]
}
|
gem-squad_v2-train-111176
|
573195dbe6313a140071d0e2
|
Religion_in_ancient_Rome
|
In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. Augustus, the first Roman emperor, justified the novelty of one-man rule with a vast program of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Imperial cult became one of the major ways in which Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Rejection of the state religion was tantamount to treason. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.
|
For whose well being were public vows made in the empire?
|
For whose well being were public vows made in the empire?
|
[
"For whose well being were public vows made in the empire?"
] |
{
"text": [
"emperor"
],
"answer_start": [
340
]
}
|
gem-squad_v2-train-111177
|
573195dbe6313a140071d0e3
|
Religion_in_ancient_Rome
|
In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. Augustus, the first Roman emperor, justified the novelty of one-man rule with a vast program of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Imperial cult became one of the major ways in which Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Rejection of the state religion was tantamount to treason. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.
|
What did the Romans use as a means of expanding their rule throughout the empire?
|
What did the Romans use as a means of expanding their rule throughout the empire?
|
[
"What did the Romans use as a means of expanding their rule throughout the empire?"
] |
{
"text": [
"Imperial cult"
],
"answer_start": [
518
]
}
|
gem-squad_v2-train-111178
|
573195dbe6313a140071d0e4
|
Religion_in_ancient_Rome
|
In the wake of the Republic's collapse, state religion had adapted to support the new regime of the emperors. Augustus, the first Roman emperor, justified the novelty of one-man rule with a vast program of religious revivalism and reform. Public vows formerly made for the security of the republic now were directed at the wellbeing of the emperor. So-called "emperor worship" expanded on a grand scale the traditional Roman veneration of the ancestral dead and of the Genius, the divine tutelary of every individual. Imperial cult became one of the major ways in which Rome advertised its presence in the provinces and cultivated shared cultural identity and loyalty throughout the Empire. Rejection of the state religion was tantamount to treason. This was the context for Rome's conflict with Christianity, which Romans variously regarded as a form of atheism and novel superstitio.
|
As what during the time of the Roman empire was rejection of the state religion viewed?
|
As what during the time of the Roman empire was rejection of the state religion viewed?
|
[
"As what during the time of the Roman empire was rejection of the state religion viewed?"
] |
{
"text": [
"treason"
],
"answer_start": [
741
]
}
|
gem-squad_v2-train-111179
|
57319760e99e3014001e6174
|
Religion_in_ancient_Rome
|
Rome had a semi-divine ancestor in the Trojan refugee Aeneas, son of Venus, who was said to have established the nucleus of Roman religion when he brought the Palladium, Lares and Penates from Troy to Italy. These objects were believed in historical times to remain in the keeping of the Vestals, Rome's female priesthood. Aeneas had been given refuge by King Evander, a Greek exile from Arcadia, to whom were attributed other religious foundations: he established the Ara Maxima, "Greatest Altar," to Hercules at the site that would become the Forum Boarium, and he was the first to celebrate the Lupercalia, an archaic festival in February that was celebrated as late as the 5th century of the Christian era.
|
What mythical figure did the Romans consider to be semi-divine?
|
What mythical figure did the Romans consider to be semi-divine?
|
[
"What mythical figure did the Romans consider to be semi-divine?"
] |
{
"text": [
"Aeneas"
],
"answer_start": [
54
]
}
|
gem-squad_v2-train-111180
|
57319760e99e3014001e6175
|
Religion_in_ancient_Rome
|
Rome had a semi-divine ancestor in the Trojan refugee Aeneas, son of Venus, who was said to have established the nucleus of Roman religion when he brought the Palladium, Lares and Penates from Troy to Italy. These objects were believed in historical times to remain in the keeping of the Vestals, Rome's female priesthood. Aeneas had been given refuge by King Evander, a Greek exile from Arcadia, to whom were attributed other religious foundations: he established the Ara Maxima, "Greatest Altar," to Hercules at the site that would become the Forum Boarium, and he was the first to celebrate the Lupercalia, an archaic festival in February that was celebrated as late as the 5th century of the Christian era.
|
Of what did Aeneas establish the central feature?
|
Of what did Aeneas establish the central feature?
|
[
"Of what did Aeneas establish the central feature?"
] |
{
"text": [
"Roman religion"
],
"answer_start": [
124
]
}
|
gem-squad_v2-train-111181
|
57319760e99e3014001e6176
|
Religion_in_ancient_Rome
|
Rome had a semi-divine ancestor in the Trojan refugee Aeneas, son of Venus, who was said to have established the nucleus of Roman religion when he brought the Palladium, Lares and Penates from Troy to Italy. These objects were believed in historical times to remain in the keeping of the Vestals, Rome's female priesthood. Aeneas had been given refuge by King Evander, a Greek exile from Arcadia, to whom were attributed other religious foundations: he established the Ara Maxima, "Greatest Altar," to Hercules at the site that would become the Forum Boarium, and he was the first to celebrate the Lupercalia, an archaic festival in February that was celebrated as late as the 5th century of the Christian era.
|
Who were the keepers of Aeneas's sacred objects?
|
Who were the keepers of Aeneas's sacred objects?
|
[
"Who were the keepers of Aeneas's sacred objects?"
] |
{
"text": [
"Vestals"
],
"answer_start": [
288
]
}
|
gem-squad_v2-train-111182
|
57319760e99e3014001e6177
|
Religion_in_ancient_Rome
|
Rome had a semi-divine ancestor in the Trojan refugee Aeneas, son of Venus, who was said to have established the nucleus of Roman religion when he brought the Palladium, Lares and Penates from Troy to Italy. These objects were believed in historical times to remain in the keeping of the Vestals, Rome's female priesthood. Aeneas had been given refuge by King Evander, a Greek exile from Arcadia, to whom were attributed other religious foundations: he established the Ara Maxima, "Greatest Altar," to Hercules at the site that would become the Forum Boarium, and he was the first to celebrate the Lupercalia, an archaic festival in February that was celebrated as late as the 5th century of the Christian era.
|
What ancient festival was celebrated until the 5th century?
|
What ancient festival was celebrated until the 5th century?
|
[
"What ancient festival was celebrated until the 5th century?"
] |
{
"text": [
"Lupercalia"
],
"answer_start": [
598
]
}
|
gem-squad_v2-train-111183
|
57319760e99e3014001e6178
|
Religion_in_ancient_Rome
|
Rome had a semi-divine ancestor in the Trojan refugee Aeneas, son of Venus, who was said to have established the nucleus of Roman religion when he brought the Palladium, Lares and Penates from Troy to Italy. These objects were believed in historical times to remain in the keeping of the Vestals, Rome's female priesthood. Aeneas had been given refuge by King Evander, a Greek exile from Arcadia, to whom were attributed other religious foundations: he established the Ara Maxima, "Greatest Altar," to Hercules at the site that would become the Forum Boarium, and he was the first to celebrate the Lupercalia, an archaic festival in February that was celebrated as late as the 5th century of the Christian era.
|
To whom did Aeneas set up an alter in Rome?
|
To whom did Aeneas set up an alter in Rome?
|
[
"To whom did Aeneas set up an alter in Rome?"
] |
{
"text": [
"Hercules"
],
"answer_start": [
502
]
}
|
gem-squad_v2-train-111184
|
57319878e17f3d1400422255
|
Religion_in_ancient_Rome
|
The myth of a Trojan founding with Greek influence was reconciled through an elaborate genealogy (the Latin kings of Alba Longa) with the well-known legend of Rome's founding by Romulus and Remus. The most common version of the twins' story displays several aspects of hero myth. Their mother, Rhea Silvia, had been ordered by her uncle the king to remain a virgin, in order to preserve the throne he had usurped from her father. Through divine intervention, the rightful line was restored when Rhea Silvia was impregnated by the god Mars. She gave birth to twins, who were duly exposed by order of the king but saved through a series of miraculous events.
|
What mythical characters were involved in the founding of Rome?
|
What mythical characters were involved in the founding of Rome?
|
[
"What mythical characters were involved in the founding of Rome?"
] |
{
"text": [
"Romulus and Remus"
],
"answer_start": [
178
]
}
|
gem-squad_v2-train-111185
|
57319878e17f3d1400422256
|
Religion_in_ancient_Rome
|
The myth of a Trojan founding with Greek influence was reconciled through an elaborate genealogy (the Latin kings of Alba Longa) with the well-known legend of Rome's founding by Romulus and Remus. The most common version of the twins' story displays several aspects of hero myth. Their mother, Rhea Silvia, had been ordered by her uncle the king to remain a virgin, in order to preserve the throne he had usurped from her father. Through divine intervention, the rightful line was restored when Rhea Silvia was impregnated by the god Mars. She gave birth to twins, who were duly exposed by order of the king but saved through a series of miraculous events.
|
What type of story was the Romulus and Remus tale?
|
What type of story was the Romulus and Remus tale?
|
[
"What type of story was the Romulus and Remus tale?"
] |
{
"text": [
"hero myth"
],
"answer_start": [
269
]
}
|
gem-squad_v2-train-111186
|
57319878e17f3d1400422257
|
Religion_in_ancient_Rome
|
The myth of a Trojan founding with Greek influence was reconciled through an elaborate genealogy (the Latin kings of Alba Longa) with the well-known legend of Rome's founding by Romulus and Remus. The most common version of the twins' story displays several aspects of hero myth. Their mother, Rhea Silvia, had been ordered by her uncle the king to remain a virgin, in order to preserve the throne he had usurped from her father. Through divine intervention, the rightful line was restored when Rhea Silvia was impregnated by the god Mars. She gave birth to twins, who were duly exposed by order of the king but saved through a series of miraculous events.
|
Who was the mother of Romulus and Remus?
|
Who was the mother of Romulus and Remus?
|
[
"Who was the mother of Romulus and Remus?"
] |
{
"text": [
"Rhea Silvia"
],
"answer_start": [
294
]
}
|
gem-squad_v2-train-111187
|
57319878e17f3d1400422258
|
Religion_in_ancient_Rome
|
The myth of a Trojan founding with Greek influence was reconciled through an elaborate genealogy (the Latin kings of Alba Longa) with the well-known legend of Rome's founding by Romulus and Remus. The most common version of the twins' story displays several aspects of hero myth. Their mother, Rhea Silvia, had been ordered by her uncle the king to remain a virgin, in order to preserve the throne he had usurped from her father. Through divine intervention, the rightful line was restored when Rhea Silvia was impregnated by the god Mars. She gave birth to twins, who were duly exposed by order of the king but saved through a series of miraculous events.
|
What god was the father of Romulus and Remus?
|
What god was the father of Romulus and Remus?
|
[
"What god was the father of Romulus and Remus?"
] |
{
"text": [
"Mars"
],
"answer_start": [
534
]
}
|
gem-squad_v2-train-111188
|
57319878e17f3d1400422259
|
Religion_in_ancient_Rome
|
The myth of a Trojan founding with Greek influence was reconciled through an elaborate genealogy (the Latin kings of Alba Longa) with the well-known legend of Rome's founding by Romulus and Remus. The most common version of the twins' story displays several aspects of hero myth. Their mother, Rhea Silvia, had been ordered by her uncle the king to remain a virgin, in order to preserve the throne he had usurped from her father. Through divine intervention, the rightful line was restored when Rhea Silvia was impregnated by the god Mars. She gave birth to twins, who were duly exposed by order of the king but saved through a series of miraculous events.
|
What type of events saved the twins of Roman myth?
|
What type of events saved the twins of Roman myth?
|
[
"What type of events saved the twins of Roman myth?"
] |
{
"text": [
"miraculous"
],
"answer_start": [
638
]
}
|
gem-squad_v2-train-111189
|
573199ecb9d445190005e3fd
|
Religion_in_ancient_Rome
|
Romulus was credited with several religious institutions. He founded the Consualia festival, inviting the neighbouring Sabines to participate; the ensuing rape of the Sabine women by Romulus's men further embedded both violence and cultural assimilation in Rome's myth of origins. As a successful general, Romulus is also supposed to have founded Rome's first temple to Jupiter Feretrius and offered the spolia opima, the prime spoils taken in war, in the celebration of the first Roman triumph. Spared a mortal's death, Romulus was mysteriously spirited away and deified.
|
What type of organization did Romulus establish?
|
What type of organization did Romulus establish?
|
[
"What type of organization did Romulus establish?"
] |
{
"text": [
"religious"
],
"answer_start": [
34
]
}
|
gem-squad_v2-train-111190
|
573199ecb9d445190005e3fe
|
Religion_in_ancient_Rome
|
Romulus was credited with several religious institutions. He founded the Consualia festival, inviting the neighbouring Sabines to participate; the ensuing rape of the Sabine women by Romulus's men further embedded both violence and cultural assimilation in Rome's myth of origins. As a successful general, Romulus is also supposed to have founded Rome's first temple to Jupiter Feretrius and offered the spolia opima, the prime spoils taken in war, in the celebration of the first Roman triumph. Spared a mortal's death, Romulus was mysteriously spirited away and deified.
|
What religious festival did Romulus found?
|
What religious festival did Romulus found?
|
[
"What religious festival did Romulus found?"
] |
{
"text": [
"Consualia"
],
"answer_start": [
73
]
}
|
gem-squad_v2-train-111191
|
573199ecb9d445190005e3ff
|
Religion_in_ancient_Rome
|
Romulus was credited with several religious institutions. He founded the Consualia festival, inviting the neighbouring Sabines to participate; the ensuing rape of the Sabine women by Romulus's men further embedded both violence and cultural assimilation in Rome's myth of origins. As a successful general, Romulus is also supposed to have founded Rome's first temple to Jupiter Feretrius and offered the spolia opima, the prime spoils taken in war, in the celebration of the first Roman triumph. Spared a mortal's death, Romulus was mysteriously spirited away and deified.
|
According to myth, what god's temple did Romulus found?
|
According to myth, what god's temple did Romulus found?
|
[
"According to myth, what god's temple did Romulus found?"
] |
{
"text": [
"Jupiter"
],
"answer_start": [
370
]
}
|
gem-squad_v2-train-111192
|
573199ecb9d445190005e400
|
Religion_in_ancient_Rome
|
Romulus was credited with several religious institutions. He founded the Consualia festival, inviting the neighbouring Sabines to participate; the ensuing rape of the Sabine women by Romulus's men further embedded both violence and cultural assimilation in Rome's myth of origins. As a successful general, Romulus is also supposed to have founded Rome's first temple to Jupiter Feretrius and offered the spolia opima, the prime spoils taken in war, in the celebration of the first Roman triumph. Spared a mortal's death, Romulus was mysteriously spirited away and deified.
|
What did Romulus offer to Jupiter in the first Roman Triumph?
|
What did Romulus offer to Jupiter in the first Roman Triumph?
|
[
"What did Romulus offer to Jupiter in the first Roman Triumph?"
] |
{
"text": [
"spoils taken in war"
],
"answer_start": [
428
]
}
|
gem-squad_v2-train-111193
|
573199ecb9d445190005e401
|
Religion_in_ancient_Rome
|
Romulus was credited with several religious institutions. He founded the Consualia festival, inviting the neighbouring Sabines to participate; the ensuing rape of the Sabine women by Romulus's men further embedded both violence and cultural assimilation in Rome's myth of origins. As a successful general, Romulus is also supposed to have founded Rome's first temple to Jupiter Feretrius and offered the spolia opima, the prime spoils taken in war, in the celebration of the first Roman triumph. Spared a mortal's death, Romulus was mysteriously spirited away and deified.
|
Instead of death, what happened to Romulus?
|
Instead of death, what happened to Romulus?
|
[
"Instead of death, what happened to Romulus?"
] |
{
"text": [
"deified"
],
"answer_start": [
564
]
}
|
gem-squad_v2-train-111194
|
57319b91e17f3d1400422269
|
Religion_in_ancient_Rome
|
Each of Rome's legendary or semi-legendary kings was associated with one or more religious institutions still known to the later Republic. Tullus Hostilius and Ancus Marcius instituted the fetial priests. The first "outsider" Etruscan king, Lucius Tarquinius Priscus, founded a Capitoline temple to the triad Jupiter, Juno and Minerva which served as the model for the highest official cult throughout the Roman world. The benevolent, divinely fathered Servius Tullius established the Latin League, its Aventine Temple to Diana, and the Compitalia to mark his social reforms. Servius Tullius was murdered and succeeded by the arrogant Tarquinius Superbus, whose expulsion marked the beginning of Rome as a republic with annually elected magistrates.
|
To what were the first kings of Rome associated?
|
To what were the first kings of Rome associated?
|
[
"To what were the first kings of Rome associated?"
] |
{
"text": [
"religious institutions"
],
"answer_start": [
81
]
}
|
gem-squad_v2-train-111195
|
57319b91e17f3d140042226a
|
Religion_in_ancient_Rome
|
Each of Rome's legendary or semi-legendary kings was associated with one or more religious institutions still known to the later Republic. Tullus Hostilius and Ancus Marcius instituted the fetial priests. The first "outsider" Etruscan king, Lucius Tarquinius Priscus, founded a Capitoline temple to the triad Jupiter, Juno and Minerva which served as the model for the highest official cult throughout the Roman world. The benevolent, divinely fathered Servius Tullius established the Latin League, its Aventine Temple to Diana, and the Compitalia to mark his social reforms. Servius Tullius was murdered and succeeded by the arrogant Tarquinius Superbus, whose expulsion marked the beginning of Rome as a republic with annually elected magistrates.
|
To what group of deities did Lucius Tarquinius Priscus establish a temple?
|
To what group of deities did Lucius Tarquinius Priscus establish a temple?
|
[
"To what group of deities did Lucius Tarquinius Priscus establish a temple?"
] |
{
"text": [
"Jupiter, Juno and Minerva"
],
"answer_start": [
309
]
}
|
gem-squad_v2-train-111196
|
57319b91e17f3d140042226b
|
Religion_in_ancient_Rome
|
Each of Rome's legendary or semi-legendary kings was associated with one or more religious institutions still known to the later Republic. Tullus Hostilius and Ancus Marcius instituted the fetial priests. The first "outsider" Etruscan king, Lucius Tarquinius Priscus, founded a Capitoline temple to the triad Jupiter, Juno and Minerva which served as the model for the highest official cult throughout the Roman world. The benevolent, divinely fathered Servius Tullius established the Latin League, its Aventine Temple to Diana, and the Compitalia to mark his social reforms. Servius Tullius was murdered and succeeded by the arrogant Tarquinius Superbus, whose expulsion marked the beginning of Rome as a republic with annually elected magistrates.
|
Where was the temple to the triad gods established?
|
Where was the temple to the triad gods established?
|
[
"Where was the temple to the triad gods established?"
] |
{
"text": [
"Capitoline"
],
"answer_start": [
278
]
}
|
gem-squad_v2-train-111197
|
57319b91e17f3d140042226c
|
Religion_in_ancient_Rome
|
Each of Rome's legendary or semi-legendary kings was associated with one or more religious institutions still known to the later Republic. Tullus Hostilius and Ancus Marcius instituted the fetial priests. The first "outsider" Etruscan king, Lucius Tarquinius Priscus, founded a Capitoline temple to the triad Jupiter, Juno and Minerva which served as the model for the highest official cult throughout the Roman world. The benevolent, divinely fathered Servius Tullius established the Latin League, its Aventine Temple to Diana, and the Compitalia to mark his social reforms. Servius Tullius was murdered and succeeded by the arrogant Tarquinius Superbus, whose expulsion marked the beginning of Rome as a republic with annually elected magistrates.
|
What organization did Servius Tullius found?
|
What organization did Servius Tullius found?
|
[
"What organization did Servius Tullius found?"
] |
{
"text": [
"Latin League,"
],
"answer_start": [
485
]
}
|
gem-squad_v2-train-111198
|
57319b91e17f3d140042226d
|
Religion_in_ancient_Rome
|
Each of Rome's legendary or semi-legendary kings was associated with one or more religious institutions still known to the later Republic. Tullus Hostilius and Ancus Marcius instituted the fetial priests. The first "outsider" Etruscan king, Lucius Tarquinius Priscus, founded a Capitoline temple to the triad Jupiter, Juno and Minerva which served as the model for the highest official cult throughout the Roman world. The benevolent, divinely fathered Servius Tullius established the Latin League, its Aventine Temple to Diana, and the Compitalia to mark his social reforms. Servius Tullius was murdered and succeeded by the arrogant Tarquinius Superbus, whose expulsion marked the beginning of Rome as a republic with annually elected magistrates.
|
The removal of whom marked the beginning of the Roman Republic?
|
The removal of whom marked the beginning of the Roman Republic?
|
[
"The removal of whom marked the beginning of the Roman Republic?"
] |
{
"text": [
"Tarquinius Superbus"
],
"answer_start": [
635
]
}
|
gem-squad_v2-train-111199
|
5731a18fe17f3d140042228b
|
Religion_in_ancient_Rome
|
Rome offers no native creation myth, and little mythography to explain the character of its deities, their mutual relationships or their interactions with the human world, but Roman theology acknowledged that di immortales (immortal gods) ruled all realms of the heavens and earth. There were gods of the upper heavens, gods of the underworld and a myriad of lesser deities between. Some evidently favoured Rome because Rome honoured them, but none were intrinsically, irredeemably foreign or alien. The political, cultural and religious coherence of an emergent Roman super-state required a broad, inclusive and flexible network of lawful cults. At different times and in different places, the sphere of influence, character and functions of a divine being could expand, overlap with those of others, and be redefined as Roman. Change was embedded within existing traditions.
|
What type of myth did Rome not have?
|
What type of myth did Rome not have?
|
[
"What type of myth did Rome not have?"
] |
{
"text": [
"creation"
],
"answer_start": [
22
]
}
|
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