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In mathematics, a right group is an algebraic structure consisting of a set together with a binary operation that combines two elements into a third element while obeying the right group axioms. The right group axioms are similar to the group axioms, but while groups can have only one identity and any element can have only one inverse, right groups allow for multiple one-sided identity elements and multiple one-sided inverse elements.
It can be proven (theorem 1 | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, in semigroup theory, a Schützenberger group is a certain group associated with a Green H-class of a semigroup. The Schützenberger groups associated with different H-classes are different. However, the groups associated with two different H-classes contained in the same D-class of a semigroup are isomorphic | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily the elementary arithmetic multiplication): x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup | https://huggingface.co/datasets/fmars/wiki_stem |
In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations. The terminology conveys the idea that the elements of the semigroup are acting as transformations of the set. From an algebraic perspective, a semigroup action is a generalization of the notion of a group action in group theory | https://huggingface.co/datasets/fmars/wiki_stem |
Semigroup Forum (print ISSN 0037-1912, electronic ISSN 1432-2137) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of information on current research in semigroup theory. Coverage in the journal includes: algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, transformation semigroups, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, and logic | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic example would be the three integers 0, 1, and −1, together with the operation of multiplication. Multiplication of integers is associative, and the product of any two of these three integers is again one of these three integers | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having two elements:
O2, the null semigroup of order two,
LO2, the left zero semigroup of order two,
RO2, the right zero semigroup of order two,
({0,1}, ∧) (where "∧" is the logical connective "and"), or equivalently the set {0,1} under multiplication: the only semilattice with two elements and the only non-null semigroup with zero of order two, also a monoid, and ultimately the two-element Boolean algebra,
(Z2, +2) (where Z2 = {0,1} and "+2" is "addition modulo 2"), or equivalently ({0,1}, ⊕) (where "⊕" is the logical connective "xor"), or equivalently the set {−1,1} under multiplication: the only group of order two. The semigroups LO2 and RO2 are antiisomorphic | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a skew lattice is an algebraic structure that is a non-commutative generalization of a lattice. While the term skew lattice can be used to refer to any non-commutative generalization of a lattice, since 1989 it has been used primarily as follows.
Definition
A skew lattice is a set S equipped with two associative, idempotent binary operations
∧
{\displaystyle \wedge }
and
∨
{\displaystyle \vee }
, called meet and join, that validate the following dual pair of absorption laws
Given that
∨
{\displaystyle \vee }
and
∧
{\displaystyle \wedge }
are associative and idempotent, these identities are equivalent to validating the following dual pair of statements:
Historical background
For over 60 years, noncommutative variations of lattices have been studied with differing motivations | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that ab = ba for all elements a and b in the semigroup | https://huggingface.co/datasets/fmars/wiki_stem |
Strong measurability has a number of different meanings, some of which are explained below.
Values in Banach spaces
For a function f with values in a Banach space (or Fréchet space), strong measurability usually means Bochner measurability.
However, if the values of f lie in the space
L
(
X
,
Y
)
{\displaystyle {\mathcal {L}}(X,Y)}
of continuous linear operators from X to Y, then often strong measurability means that the operator f(x) is Bochner measurable for each fixed x in the domain of f, whereas the Bochner measurability of f is called uniform measurability (cf | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, the set of all partial bijections on a set X (a. k. a | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and computer science, the syntactic monoid
M
(
L
)
{\displaystyle M(L)}
of a formal language
L
{\displaystyle L}
is the smallest monoid that recognizes the language
L
{\displaystyle L}
.
Syntactic quotient
The free monoid on a given set is the monoid whose elements are all the strings of zero or more elements from that set, with string concatenation as the monoid operation and the empty string as the identity element. Given a subset
S
{\displaystyle S}
of a free monoid
M
{\displaystyle M}
, one may define sets that consist of formal left or right inverses of elements in
S
{\displaystyle S}
| https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set
T
{\displaystyle T}
, for every
p
∈
N
{\displaystyle p\in \mathbb {N} }
, there is some
n
∈
N
{\displaystyle n\in \mathbb {N} }
such that
{
n
,
n
+
1
,
n
+
2
,
.
| https://huggingface.co/datasets/fmars/wiki_stem |
In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order, but allowing certain reshufflings to take place. Traces were introduced by Pierre Cartier and Dominique Foata in 1969 to give a combinatorial proof of MacMahon's master theorem | https://huggingface.co/datasets/fmars/wiki_stem |
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under function composition. If it includes the identity function, it is a monoid, called a transformation (or composition) monoid. This is the semigroup analogue of a permutation group | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element, then the Cayley table of S is
The only element in S is the zero element 0 of S and is also the identity element 1 of S | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups having some nice algebraic properties. Those classes can be defined in two distinct ways, using either algebraic notions or topological notions. Varieties of finite monoids, varieties of finite ordered semigroups and varieties of finite ordered monoids are defined similarly | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the term weak inverse is used with several meanings.
Theory of semigroups
In the theory of semigroups, a weak inverse of an element x in a semigroup (S, •) is an element y such that y • x • y = y. If every element has a weak inverse, the semigroup is called an E-inversive or E-dense semigroup | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, an additive monoid
(
M
,
0
,
+
)
{\displaystyle (M,0,+)}
is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally:
(
∀
a
,
b
∈
M
)
a
+
b
=
0
⟹
a
=
b
=
0
{\displaystyle (\forall a,b\in M)\ a+b=0\implies a=b=0\!}
This means that the only way zero can be expressed as a sum is as
0
+
0
{\displaystyle 0+0}
.
References
Wehrung, Friedrich (1996) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the adele ring of a global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic number theory. It is the restricted product of all the completions of the global field and is an example of a self-dual topological ring.
An adele derives from a particular kind of idele | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and together they are among the most basic tools in analysing commutative rings. Complete commutative rings have a simpler structure than general ones, and Hensel's lemma applies to them | https://huggingface.co/datasets/fmars/wiki_stem |
In algebra, a linear topology on a left
A
{\displaystyle A}
-module
M
{\displaystyle M}
is a topology on
M
{\displaystyle M}
that is invariant under translations and admits a fundamental system of neighborhood of
0
{\displaystyle 0}
that consists of submodules of
M
.
{\displaystyle M. }
If there is such a topology,
M
{\displaystyle M}
is said to be linearly topologized | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, an element
z
{\displaystyle z}
of a Banach algebra
A
{\displaystyle A}
is called a topological divisor of zero if there exists a sequence
x
1
,
x
2
,
x
3
,
.
.
| https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous.
Examples
A topological vector space is a topological module over a topological field.
An abelian topological group can be considered as a topological module over
Z
,
{\displaystyle \mathbb {Z} ,}
where
Z
{\displaystyle \mathbb {Z} }
is the ring of integers with the discrete topology | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a topological ring is a ring
R
{\displaystyle R}
that is also a topological space such that both the addition and the multiplication are continuous as maps:
where
R
×
R
{\displaystyle R\times R}
carries the product topology. That means
R
{\displaystyle R}
is an additive topological group and a multiplicative topological semigroup.
Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field | https://huggingface.co/datasets/fmars/wiki_stem |
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study.
Basic idea
In universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy.
An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called scalar multiplication between elements of the field (called scalars), and elements of the vector space (called vectors) | https://huggingface.co/datasets/fmars/wiki_stem |
In logic, mathematics, and computer science, arity ( (listen)) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree | https://huggingface.co/datasets/fmars/wiki_stem |
In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner. It also represents the endomorphisms of an algebra by certain indexings of algebra elements, which can correspond to the usual matrices when the free algebra is a vector space | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, BCI and BCK algebras are algebraic structures in universal algebra, which were introduced by Y. Imai, K. Iséki and S | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a closure operator on a set S is a function
cl
:
P
(
S
)
→
P
(
S
)
{\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal {P}}(S)}
from the power set of S to itself that satisfies the following conditions for all sets
X
,
Y
⊆
S
{\displaystyle X,Y\subseteq S}
Closure operators are determined by their closed sets, i. e. , by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation.
Basic example
The prototypical example of a congruence relation is congruence modulo
n
{\displaystyle n}
on the set of integers | https://huggingface.co/datasets/fmars/wiki_stem |
In universal algebra, a congruence-permutable algebra is an algebra whose congruences commute under composition. This symmetry has several equivalent characterizations, which lend to the analysis of such algebras. Many familiar varieties of algebras, such as the variety of groups, consist of congruence-permutable algebras, but some, like the variety of lattices, have members that are not congruence-permutable | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. The larger set is then said to be generated by the smaller set | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by McNulty and Shallon, and has seen many uses in the field of universal algebra since then.
Definition
Let D = (V, E) be a directed graph, and 0 an element not in V | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a branch of mathematics, the algebraic structure group with operators or Ω-group can be viewed as a group with a set Ω that operates on the elements of the group in a special way.
Groups with operators were extensively studied by Emmy Noether and her school in the 1920s. She employed the concept in her original formulation of the three Noether isomorphism theorems | https://huggingface.co/datasets/fmars/wiki_stem |
Hidden algebra provides a formal semantics for use in the field of software engineering, especially for concurrent distributed object systems. It supports correctness proofs. Hidden algebra was studied by Joseph Goguen | https://huggingface.co/datasets/fmars/wiki_stem |
In universal algebra, a variety of algebras means the class of all algebraic structures of a given signature satisfying a given set of identities. One calls a variety locally finite if every finitely generated algebra has finite cardinality, or equivalently, if every finitely generated free algebra has finite cardinality.
The variety of Boolean algebras constitutes a famous example | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation.
Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is additionally compatible with all the operations of the algebra, in the formal sense described below | https://huggingface.co/datasets/fmars/wiki_stem |
In logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published a complete description of the lattice in 1941. The relative simplicity of Post's lattice is in stark contrast to the lattice of clones on a three-element (or larger) set, which has the cardinality of the continuum, and a complicated inner structure | https://huggingface.co/datasets/fmars/wiki_stem |
In logic, a pseudoelementary class is a class of structures derived from an elementary class (one definable in first-order logic) by omitting some of its sorts and relations. It is the mathematical logic counterpart of the notion in category theory of (the codomain of) a forgetful functor, and in physics of (hypothesized) hidden variable theories purporting to explain quantum mechanics. Elementary classes are (vacuously) pseudoelementary but the converse is not always true; nevertheless pseudoelementary classes share some of the properties of elementary classes such as being closed under ultraproducts | https://huggingface.co/datasets/fmars/wiki_stem |
In universal algebra, a quasi-identity is an implication of the form
s1 = t1 ∧ … ∧ sn = tn → s = twhere s1, . . | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a quasivariety is a class of algebraic structures generalizing the notion of variety by allowing equational conditions on the axioms defining the class.
Definition
A trivial algebra contains just one element. A quasivariety is a class K of algebras with a specified signature satisfying any of the following equivalent conditions | https://huggingface.co/datasets/fmars/wiki_stem |
In universal algebra and in model theory, a reduct of an algebraic structure is obtained by omitting some of the operations and relations of that structure. The opposite of "reduct" is "expansion. "
Definition
Let A be an algebraic structure (in the sense of universal algebra) or a structure in the sense of model theory, organized as a set X together with an indexed family of operations and relations φi on that set, with index set I | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a Stone algebra, or Stone lattice, is a pseudo-complemented distributive lattice such that a* ∨ a** = 1. They were introduced by Grätzer & Schmidt (1957) and named after Marshall Harvey Stone.
Boolean algebras are Stone algebras, and Stone algebras are Ockham algebras | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations.
"Algebra", when referring to a structure, often means a vector space or module equipped with an additional bilinear operation. Algebras in universal algebra are far more general: they are a common generalisation of all algebraic structures | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944 and has proved to be a powerful generalization of the notion of direct product.
Definition
A subdirect product is a subalgebra (in the sense of universal algebra) A of a direct product ΠiAi such that every induced projection (the composite pjs: A → Aj of a projection pj: ΠiAi → Aj with the subalgebra inclusion s: A → ΠiAi) is surjective | https://huggingface.co/datasets/fmars/wiki_stem |
In the branch of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras. Subdirectly irreducible algebras play a somewhat analogous role in algebra to primes in number theory.
Definition
A universal algebra A is said to be subdirectly irreducible when A has more than one element, and when any subdirect representation of A includes (as a factor) an algebra isomorphic to A, with the isomorphism being given by the projection map | https://huggingface.co/datasets/fmars/wiki_stem |
Toastmaster is a brand name for home appliances. It was originally (1921) the name of one of the world's first automatic electric pop-up toasters for home use, the Toastmaster Model 1-A-1. Since then the Toastmaster brand has been used on a wide range of small kitchen appliances, such as coffeemakers, waffle irons, toasters, and blenders | https://huggingface.co/datasets/fmars/wiki_stem |
TrueCookPlus was a microwave oven operating system developed and patented by Microwave Science JV LLC. TrueCookPlus is endorsed by the National Frozen & Refrigerated Foods Association on behalf of over 1300 US frozen food industry member companies. As of 2019, the website with all the TrueCookPlus codes, TrueCookPlus | https://huggingface.co/datasets/fmars/wiki_stem |
The Ultimate Chopper was a kitchen appliance, mainly advertised on television in the form of an As Seen On TV 30 minute infomercial, and sold on-line.
What it does
The Ultimate Chopper is mainly used for chopping and preparing food in preparation of cooking. It is also used for mixing and whipping | https://huggingface.co/datasets/fmars/wiki_stem |
Auto reignition is a process used in gas burners to control ignition devices based on whether a burner flame is lit. This information can be used to stop an ignition device from sparking, which is no longer necessary after the flame is lit. It can also be used to start the sparking device again if the flame goes out while the burner is still supplying gas, for example, from a gust of wind or vibration | https://huggingface.co/datasets/fmars/wiki_stem |
A bread making machine or breadmaker is a home appliance for baking bread. It consists of a bread pan (or "tin"), at the bottom of which are one or more built-in paddles, mounted in the center of a small special-purpose oven. The machine is usually controlled by a built-in computer using settings input via a control panel | https://huggingface.co/datasets/fmars/wiki_stem |
A butane torch is a tool which creates an intensely hot flame using a fuel mixture of LPGs typically including some percentage of butane, a flammable gas.
Consumer air butane torches are often claimed to develop flame temperatures up to approximately 1,430 °C (2,610 °F). This temperature is high enough to melt many common metals, such as aluminum and copper, and hot enough to vaporize many organic compounds as well | https://huggingface.co/datasets/fmars/wiki_stem |
A charbroiler (also referred to as a chargrill, char-broiler or simply broiler) is a commonly used cooking device consisting of a series of grates or ribs that can be heated using a variety of means, and is used in both residential and commercial applications for a variety of cooking operations. The heat source is almost always beneath the cooking surface – for gas-fired applications this is referred to as an under-fired broiler. Most commonly the charbroiler is a series of long evenly spaced metal ribs over a large combustion chamber filled with an array of burners that may have a deflector, briquettes or radiant between the burner and the cooking surface | https://huggingface.co/datasets/fmars/wiki_stem |
Barbecue varies by the type of meat, sauce, rub, or other flavorings used, the point in barbecuing at which they are added, the role smoke plays, the equipment and fuel used, cooking temperature, and cooking time.
The meat may be whole, ground (for hamburgers), or processed into sausage or kebabs. The meat may be marinated or rubbed with spices before cooking, basted with a sauce or oil before, during or after cooking, or any combination of these | https://huggingface.co/datasets/fmars/wiki_stem |
A coffee percolator is a type of pot used for the brewing of coffee by continually cycling the boiling or nearly boiling brew through the grounds using gravity until the required strength is reached. Coffee percolators once enjoyed great popularity but were supplanted in the early 1970s by automatic drip-brew coffeemakers. Percolators often expose the grounds to higher temperatures than other brewing methods, and may recirculate already brewed coffee through the beans | https://huggingface.co/datasets/fmars/wiki_stem |
A coffeemaker, coffee maker or coffee machine is a cooking appliance used to brew coffee. While there are many different types of coffeemakers, the two most common brewing principles use gravity or pressure to move hot water through coffee grounds. In the most common devices, coffee grounds are placed into a paper or metal filter inside a funnel, which is set over a glass or ceramic coffee pot, a cooking pot in the kettle family | https://huggingface.co/datasets/fmars/wiki_stem |
Combi steamers (also called combi-steamers, hot-air steamers, combination steam-convection ovens, or simply combi ovens) are combination ovens that expand upon standard convection ovens in that they can also generate conventional moist steam or superheated steam and are capable of shifting between cooking modes automatically during the cooking process. They can be used to simultaneously steam vegetables or potatoes quickly and gently, while also roasting or braising meat and fish, or baking bread. The appliance is fit for many culinary applications, including baking, roasting, grilling, steaming, braising, blanching and poaching | https://huggingface.co/datasets/fmars/wiki_stem |
A crêpe maker is a cooking device used to make crêpes, galettes, pancakes, blinis or tortillas. It should not be mistaken for a regular pan or a crêpe pan.
Origins
Crêpe makers were originally large cast-iron plates set over the fire to cook cereal-based batters | https://huggingface.co/datasets/fmars/wiki_stem |
Mint chocolate chip is an ice cream flavor composed of mint ice cream with small chocolate chips. In some cases the liqueur crème de menthe is used to provide the mint flavor, but in most cases peppermint or spearmint flavoring is used. Food coloring is usually added to make it green, but it may be beige or white in "all natural" or "organic" varieties | https://huggingface.co/datasets/fmars/wiki_stem |
Moose Tracks is a branded flavor of ice cream owned and licensed by Denali Flavors Inc. that is manufactured by different companies under various brands. The Original Moose Tracks product description is as follows, "vanilla ice cream with peanut butter cups and famous Moose Tracks fudge" | https://huggingface.co/datasets/fmars/wiki_stem |
Neapolitan ice cream, also sometimes called Harlequin ice cream, is a type of ice cream composed of three separate flavors (vanilla, chocolate, and strawberry) arranged side by side in the same container, usually without any packaging in between.
History
Neapolitan ice cream was the first type of ice cream to combine three flavors. The first recorded recipe was created by head chef of the royal Prussian household Louis Ferdinand Jungius in 1839, who dedicated the recipe to Fürst Pückler | https://huggingface.co/datasets/fmars/wiki_stem |
Oyster ice cream is a flavor of ice cream with a savory taste. After being recorded in a 19th-century cookbook, then forgotten for the next two centuries, the ice cream flavor has been offered at a number of 21st-century oyster festivals.
History
The only historical source for oyster ice cream is found in Mary Randolph's cookbook, The Virginia Housewife, published in 1824 | https://huggingface.co/datasets/fmars/wiki_stem |
Pistachio ice cream or pistachio nut ice cream is an ice cream flavor made with pistachio nuts or flavoring. It is often distinctively green in color. Pistachio is also a flavor of sorbet and gelato | https://huggingface.co/datasets/fmars/wiki_stem |
Rocky road ice cream is a chocolate flavored ice cream. Though there are variations from the original flavor, it traditionally comprises chocolate ice cream, nuts, and whole or diced marshmallows.
History
According to one source, the flavor was created in March 1929 by William Dreyer in Oakland, California when he cut up walnuts and marshmallows with his wife's sewing scissors and added them to his chocolate ice cream in a manner that reflected how his partner Joseph Edy's chocolate candy creation incorporated walnuts and marshmallow pieces | https://huggingface.co/datasets/fmars/wiki_stem |
Strawberry ice cream is a flavor of ice cream made with strawberry or strawberry flavoring. It is made by blending in fresh strawberries or strawberry flavoring with the eggs, cream, vanilla, and sugar used to make ice cream. Most strawberry ice cream is colored pink or light red | https://huggingface.co/datasets/fmars/wiki_stem |
Vanilla is frequently used to flavor ice cream, especially in North America, Asia, and Europe. Vanilla ice cream, like other flavors of ice cream, was originally created by cooling a mixture made of cream, sugar, and vanilla above a container of ice and salt. The type of vanilla used to flavor ice cream varies by location | https://huggingface.co/datasets/fmars/wiki_stem |
Herbal distillates, also known as floral waters, hydrosols, hydrolates, herbal waters, and essential waters, are aqueous products of hydrodistillation. They are colloidal suspensions of essential oils as well as water-soluble components obtained by steam distillation or hydrodistillation (a variant of steam distillation) from plants and herbs. These herbal distillates have uses as flavorings and cosmetics | https://huggingface.co/datasets/fmars/wiki_stem |
Rose water is a flavoured water made by steeping rose petals in water. It is the hydrosol portion of the distillate of rose petals, a by-product of the production of rose oil for use in perfume. Rose water is also used to flavour food, as a component in some cosmetic and medical preparations, and for religious purposes throughout Eurasia | https://huggingface.co/datasets/fmars/wiki_stem |
Oleoresins are semi-solid extracts composed of resin and essential or fatty oil, obtained by evaporation of the solvents used for their production. The oleoresin of conifers is known as crude turpentine or gum turpentine, which consists of oil of turpentine and rosin.
Properties
In contrast to essential oils obtained by steam distillation, oleoresins abound in heavier, less volatile and lipophilic compounds, such as resins, waxes, fats and fatty oils | https://huggingface.co/datasets/fmars/wiki_stem |
Hash oil or cannabis oil is an oleoresin obtained by the extraction of cannabis or hashish. It is a cannabis concentrate containing many of its resins and terpenes – in particular, tetrahydrocannabinol (THC), cannabidiol (CBD), and other cannabinoids. Hash oil is usually consumed by smoking, vaporizing or eating | https://huggingface.co/datasets/fmars/wiki_stem |
Paprika oleoresin (also known as paprika extract and oleoresin paprika) is an oil-soluble extract from the fruits of Capsicum annuum or Capsicum frutescens, and is primarily used as a colouring and/or flavouring in food products. It is composed of vegetable oil (often in the range of 97% to 98%), capsaicin, the main flavouring compound giving pungency in higher concentrations, and capsanthin and capsorubin, the main colouring compounds (among other carotenoids). It is much milder than capsicum oleoresin, often containing no capsaicin at all | https://huggingface.co/datasets/fmars/wiki_stem |
Allicin is an organosulfur compound obtained from garlic. When fresh garlic is chopped or crushed, the enzyme alliinase converts alliin into allicin, which is responsible for the aroma of fresh garlic. Allicin is unstable and quickly changes into a series of other sulfur-containing compounds such as diallyl disulfide | https://huggingface.co/datasets/fmars/wiki_stem |
Allyl isothiocyanate (AITC) is an organosulfur compound (formula CH2CHCH2NCS). The colorless oil is responsible for the pungent taste of mustard, radish, horseradish, and wasabi. This pungency and the lachrymatory effect of AITC are mediated through the TRPA1 and TRPV1 ion channels | https://huggingface.co/datasets/fmars/wiki_stem |
Gingerol ([6]-gingerol) is a phenolic phytochemical compound found in fresh ginger that activates heat receptors on the tongue. It is normally found as a pungent yellow oil in the ginger rhizome, but can also form a low-melting crystalline solid. This chemical compound is found in all members of the Zingiberaceae family and is high in concentrations in the grains of paradise as well as an African Ginger species | https://huggingface.co/datasets/fmars/wiki_stem |
Gluconasturtiin or phenethyl glucosinolate is one of the most widely distributed glucosinolates in the cruciferous vegetables, mainly in the roots, and is probably one of the plant compounds responsible for the natural pest-inhibiting properties of growing crucifers, such as cabbage, mustard or rape, in rotation with other crops. This effect of gluconasturtiin is due to its degradation by the plant enzyme myrosinase into phenethyl isothiocyanate, which is toxic to many organisms. Gluconasturtiin is named from its occurrence in watercress (Nasturtium officinale) | https://huggingface.co/datasets/fmars/wiki_stem |
Lenthionine is a cyclic organosulfur compound found in shiitake mushrooms, onions, and garlic, and it is partly responsible for their flavor. The mechanism of its formation is unclear, but it likely involves the enzyme C–S lyase.
Preparation
Lenthionine has been isolated from mushrooms by submerging them in water and allowing them to set overnight | https://huggingface.co/datasets/fmars/wiki_stem |
Piperine, along with its isomer chavicine, is the compound responsible for the pungency of black pepper and long pepper. It has been used in some forms of traditional medicine.
Preparation
Due to its poor solubility in water, piperine is typically extracted from black pepper by using organic solvents like dichloromethane | https://huggingface.co/datasets/fmars/wiki_stem |
Polygodial is chemical compound found in dorrigo pepper, mountain pepper, horopito, canelo, paracress, water-pepper, and Dendrodoris limbata. Chemically it is a drimane-type sesquiterpene dialdehyde of formula C15H22O2.
It elicits a warm and pungent flavour | https://huggingface.co/datasets/fmars/wiki_stem |
syn-Propanethial S-oxide (or (Z)-propanethial S-oxide), a member of a class of organosulfur compounds known as thiocarbonyl S-oxides (formerly "sulfines"), is a volatile liquid that acts as a lachrymatory agent (triggers tearing and stinging on contact with the eyes). The chemical is released from onions, Allium cepa, as they are sliced. The release is due to the breaking open of the onion cells and their releasing enzymes called alliinases, which then break down amino acid sulfoxides, generating sulfenic acids | https://huggingface.co/datasets/fmars/wiki_stem |
Shogaols are pungent constituents of ginger similar in chemical structure to gingerol. The most common of the group is [6]-shogaol. Like zingerone, it is produced when ginger is dried or cooked | https://huggingface.co/datasets/fmars/wiki_stem |
Sinigrin or allyl glucosinolate is a glucosinolate that belongs to the family of glucosides found in some plants of the family Brassicaceae such as Brussels sprouts, broccoli, and the seeds of black mustard (Brassica nigra). Whenever sinigrin-containing plant tissue is crushed or otherwise damaged, the enzyme myrosinase degrades sinigrin to a mustard oil (allyl isothiocyanate), which is responsible for the pungent taste of mustard and horseradish. Seeds of white mustard, Sinapis alba, give a less pungent mustard because this species contains a different glucosinolate, sinalbin | https://huggingface.co/datasets/fmars/wiki_stem |
Vinyldithiins, more precisely named 3-vinyl-4H-1,2-dithiin and 2-vinyl-4H-1,3-dithiin, are organosulfur phytochemicals formed in the breakdown of allicin from crushed garlic (Allium sativum). Vinyldithiins are Diels-Alder dimers of thioacrolein, H2C=CHCH=S, formed in turn by decomposition of allicin. In garlic supplements, vinyldithiins are only found in garlic oil macerates that are made by incubation of crushed garlic in oil | https://huggingface.co/datasets/fmars/wiki_stem |
Zingerone, also called vanillylacetone, is a major flavor component of ginger, providing the sweet flavor of cooked ginger. Zingerone is a crystalline solid that is sparingly soluble in water and soluble in ether.
Zingerone is similar in chemical structure to other flavor chemicals such as vanillin and eugenol | https://huggingface.co/datasets/fmars/wiki_stem |
A sweetener is a substance added to food or drink to impart the flavor of sweetness, either because it contains a type of sugar, or because it contains a sweet-tasting sugar substitute. Various natural non-sugar sweeteners and artificial sweeteners are used to produced food and drink.
Description
A sweetener is a substance added to food or drink to impart the flavor of sweetness, either because it contains a type of sugar, or because it contains a sweet-tasting sugar substitute | https://huggingface.co/datasets/fmars/wiki_stem |
Malt is germinated cereal grain that has been made to germinate by soaking in water and is then halted from germinating further by drying with hot air, a process known as "malting".
Malted grain is used to make beer, whisky, malted milk, malt vinegar, confections such as Maltesers and Whoppers, flavored drinks such as Horlicks, Ovaltine, and Milo, and some baked goods, such as malt loaf, bagels, and Rich Tea biscuits. Malted grain that has been ground into a coarse meal is known as "sweet meal" | https://huggingface.co/datasets/fmars/wiki_stem |
Maltodextrin is a polysaccharide that is used as a food ingredient. It is produced from grain starch by partial hydrolysis and is usually found as a white hygroscopic spray-dried powder. Maltodextrin is easily digestible, being absorbed as rapidly as glucose and may be either moderately sweet or almost flavorless (depending on the degree of polymerisation) | https://huggingface.co/datasets/fmars/wiki_stem |
In the alcoholic beverages industry, congeners are substances, other than the desired type of alcohol, ethanol, produced during fermentation. These substances include small amounts of chemicals such as methanol and other alcohols (known as fusel alcohols), acetone, acetaldehyde, esters, tannins, and aldehydes (e. g | https://huggingface.co/datasets/fmars/wiki_stem |
Gymnemic acids are a class of chemical compounds isolated from the leaves of Gymnema sylvestre (Asclepiadaceae). They are anti-sweet compounds, or sweetness inhibitors. After chewing the leaves, solutions sweetened with sugar taste like water | https://huggingface.co/datasets/fmars/wiki_stem |
Homoeriodictyol is a bitter-masking flavanone extracted from Yerba Santa (Eriodictyon californicum) a plant growing in America. Homoeriodictyol (3`-methoxy-4`,5,7-trihydroxyflavanone) is one of the 4 flavanones identified by Symrise in this plant eliciting taste-modifying property: homoeriodictyol sodium salt, eriodictyol and sterubin. Homoeriodictyol Sodium salt elicited the most potent bitter-masking activity by reducing from 10 to 40% the bitterness of salicin, amarogentin, paracetamol and quinine | https://huggingface.co/datasets/fmars/wiki_stem |
Lactisole is the sodium salt and commonly supplied form of 2-(4-methoxyphenoxy)propionic acid, a natural carboxylic acid found in roasted coffee beans. Like gymnemic acid, it has the property of masking sweet flavors and is used for this purpose in the food industry.
Chemistry
Chemically, lactisole is a double ether of hydroquinone | https://huggingface.co/datasets/fmars/wiki_stem |
A palate cleanser is a serving of food or drink that removes food residue from the tongue allowing one to more accurately assess a new flavor.
Palate cleansers are often used between tasting wine or cheese or other strong flavors. Pickled ginger is used as a palate cleanser between sushi pieces | https://huggingface.co/datasets/fmars/wiki_stem |
Ziziphin, a triterpene glycoside which exhibits taste-modifying properties, has been isolated from the leaves of Ziziphus jujuba (Rhamnaceae).
Among ziziphin's known homologues found in this plant, it is the most anti-sweet. However, its anti-sweet activity is less effective than gymnemic acid 1, another anti-sweet compound glycoside isolated from the leaves of Gymnema sylvestre (Asclepiadaceae) | https://huggingface.co/datasets/fmars/wiki_stem |
Enfleurage is a process that uses odorless fats that are solid at room temperature to capture the fragrant compounds exuded by plants. The process can be "cold" enfleurage or "hot" enfleurage.
Process
There are two types of processes:
In cold enfleurage, a large framed plate of glass, called a chassis, is smeared with a layer of animal fat, usually lard or tallow (from pork or beef, respectively), and allowed to set | https://huggingface.co/datasets/fmars/wiki_stem |
An extract (essence) is a substance made by extracting a part of a raw material, often by using a solvent such as ethanol, oil or water. Extracts may be sold as tinctures, absolutes or in powder form.
The aromatic principles of many spices, nuts, herbs, fruits, etc | https://huggingface.co/datasets/fmars/wiki_stem |
Fragrance extraction refers to the separation process of aromatic compounds from raw materials, using methods such as distillation, solvent extraction, expression, sieving, or enfleurage. The results of the extracts are either essential oils, absolutes, concretes, or butters, depending on the amount of waxes in the extracted product.
To a certain extent, all of these techniques tend to produce an extract with an aroma that differs from the aroma of the raw materials | https://huggingface.co/datasets/fmars/wiki_stem |
Gustatory technology is the engineering discipline dealing with gustatory representation.
Description
Virtual taste refers to a taste experience generated by a digital taste simulator. Electrodes are used to simulate the taste and feel of real food in the mouth | https://huggingface.co/datasets/fmars/wiki_stem |
Headspace technology is a technique developed in the 1980s to elucidate the odor compounds present in the air surrounding various objects. Usually the objects of interest are odoriferous objects such as plants, flowers and foods. Similar techniques are also used to analyze the interesting scents of locations and environments such as tea shops and saw mills | https://huggingface.co/datasets/fmars/wiki_stem |
Liquid–liquid extraction (LLE), also known as solvent extraction and partitioning, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an organic solvent (non-polar). There is a net transfer of one or more species from one liquid into another liquid phase, generally from aqueous to organic. The transfer is driven by chemical potential, i | https://huggingface.co/datasets/fmars/wiki_stem |
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