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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
9bc8ac8e4bccd5af3db1398e951138a6f15da527	besides writing the following books, waldstein also published	besides writing the following books, waldstein also published in journals numerous reports on his excavations. he wrote three short stories under the pseudonym 'gordon seymour' which were later released under his own name as the surface of things (1899).	wikipedia
ece513f271f849ead83d3473c71b0a669257eb36	he married florence, daughter of d. l. einstein	he married florence, daughter of d. l. einstein and widow of theodore seligman, in 1909. they had one son, henry, and a daughter, evelyn sophie alexandra, who married the judge sir patrick browne. he changed his surname to walston in 1918 and died in 1927 whilst on a mediterranean cruise.	wikipedia
b7d0c548b4e7aa25eecbf6218c0b6b12119be50e	waldstein was educated at columbia university (a.m., 1873),	waldstein was educated at columbia university (a.m., 1873), and also studied at heidelberg (ph.d., 1875). in 1880, he became university lecturer on classical archaeology at cambridge university, and in 1883 university reader. from 1883 to 1889 he was director of the fitzwilliam museum. in 1889 he was called to athens a...	wikipedia
3f9d6649b2fefdcca1d2f1a69439b366a9e70b38	waldstein was born into a jewish family in	waldstein was born into a jewish family in new york city, united states, on march 30, 1856, third son of henry waldstein, a merchant, and sophie, daughter of l. srisheim, of new york. he was of austrian descent.	wikipedia
0ff5c1f9f440d45d0ed1134ec7d75edc18657b36	sir charles waldstein (march 30, 1856 – march	sir charles waldstein (march 30, 1856 – march 21, 1927), known as sir charles walston from 1918 to 1927, was an anglo - american archaeologist. he also competed at the 1896 summer olympics in athens.	wikipedia
48d2b3f9e545e6d51a4edc2f983d0b785c4708fb	arif erdem is a turkish retired football manager	arif erdem is a turkish retired football manager and former professional player who played in the forward position. starting out with local club zeytinburnuspor in 1990, erdem had a decorated 15-year professional career. he scored 106 goals in 341 league matches and finished joint top scorer of the süper lig with İlhan...	wikipedia
629669ec62a1c1e56f545793dab636848fe73e41	erdem is of albanian descent, through his parents	erdem is of albanian descent, through his parents who left kumanovo. arif erdem reportedly fled to greece in 2016 after the failed turkish coup of 2016, due to his supposed links to the gülen movement, categorized by the turkish government as a terrorist organization.	wikipedia
78a83296eb50286e888b24602365d81222fa0e31	erdem had been an assistant coach with İstanbul	erdem had been an assistant coach with İstanbul büyükşehir belediyespor since 2006. on 18 november 2011, after the assignation of abdullah avcı to turkey national football team, he became the new head coach of İstanbul büyükşehir belediyespor. at the end of the season, his contract was terminated by club at 14 may 2012...	wikipedia
c798fde5f1bf735063509ad26dc43ba8405f274b	an exceptional moment of his international career came	an exceptional moment of his international career came during the uefa euro 2000 qualification, he netted three times within three minutes against northern ireland. turkey qualified and erdem was included in squad. he was a significant part of the team, especially in a winning clash against co-host belgium. during the ...	wikipedia
ac44602b63f4e0d96d42d1883db55baa787e8e6b	erdem began his international career with the turkey	erdem began his international career with the turkey u21 national team in 1991, scoring one goal in 10 caps. he participated in the akdeniz cup with the turkish olympic team in 1993, and earned his first senior team cap in 1994. two years later, turkey qualified for euro 1996. he was called up, but turkey didn't achiev...	wikipedia
904de00d4b049534477eb7131795ceacf63a9847	erdem left galatasaray for real sociedad at the	erdem left galatasaray for real sociedad at the start of the 2000–01. however, he regretted joining the club, saying "the only thing i wanted was to move to a european team... i didn't even think about it, i signed the first offer i received." erdem was plagued by injuries during his tenure, and he left the spanish clu...	wikipedia
ee3986b877b75f04f1d34ccdb7892411066953d6	erdem played for zeytinburnuspor before signing his first	erdem played for zeytinburnuspor before signing his first professional contract with galatasaray on 1 june 1991. he made 29 total appearances in his first season with the club, scoring four goals. erdem made fewer appearances the following season, providing four goals in 18 appearances as the club achieved a domestic t...	wikipedia
67c1a4ce99b4966a5eefea1887a940913f2bb904	during his 14 years with galatasaray, erdem won	during his 14 years with galatasaray, erdem won seven süper lig titles and five turkish cup titles, as well as the uefa cup in 2000. he was a part of the turkey national team that finished third at the 2002 fifa world cup. erdem was capped 60 times, scoring eleven goals.	wikipedia
27e56bd33432c3becca51dd586cdb7935d8eb566	arif erdem (born 2 january 1972) is a	arif erdem (born 2 january 1972) is a turkish retired football manager and former professional player who played in the forward position. starting out with local club zeytinburnuspor in 1990, erdem had a decorated 15-year professional career. he scored 106 goals in 341 league matches and finished joint top scorer (gol ...	wikipedia
4829e330930430632b36b35f0c5fd0d8995db978	eugène jacob de cordemoy was french physician and	eugène jacob de cordemoy was french physician and botanist. he had a particular interest in orchids, continuing the work of charles frappier. he is the author of flore de l'île de la réunion published in 1895. he also studied birds.	wikipedia
2778b099febdbc9543ec41f1ca18886c8340e8f7	he had a particular interest in orchids, continuing	he had a particular interest in orchids, continuing the work of charles frappier. he is the author of flore de l'île de la réunion (english: flora of the island of réunion) published in 1895. he also studied birds.	wikipedia
5e92afa97613ebc8b29e241e6eb42beb9e865cde	in linear algebra, a linear relation, or simply	in linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution. more precisely, if e 1 , … , e n are elements of a (left) module m over a ring r, a relation between e 1 , … , e n is a sequence of elements of r such that...	wikipedia
7fcb1d4aaebc1ca9adfc916b61eaa12f77dda9d3	in linear algebra, a linear relation, or simply	and that every submodule of a finitely generated free k[x] module is also free. the construction of higher order syzygy modules is generalized as the definition of free resolutions, which allows restating hilbert's syzygy theorem as a polynomial ring in n indeterminates over a field has global homological dimension n....	wikipedia
6431aba6f6dc31f9ba68d117d8985f0dbac23292	then, the word syzygy was popularized (among mathematicians)	then, the word syzygy was popularized (among mathematicians) by david hilbert in his 1890 article, which contains three fundamental theorems on polynomials, hilbert's syzygy theorem, hilbert's basis theorem and hilbert's nullstellensatz.	wikipedia
b1e8a6210870c8f0017a805b2347ee713b2f43b8	the word syzygy came into mathematics with the	the word syzygy came into mathematics with the work of arthur cayley. in that paper, cayley used it in the theory of resultants and discriminants. as the word syzygy was used in astronomy to denote a linear relation between planets, cayley used it to denote linear relations between minors of a matrix, such as, in the c...	wikipedia
4e53ee49f387f0aef1ecb3b631c2daf7f3288707	such that x i = g j, {\displaystyle	such that x i = g j, {\displaystyle x_{i}=g_{j},} x j = − g i, {\displaystyle x_{j}=-g_{i},} and x h = 0 {\displaystyle x_{h}=0} otherwise.	wikipedia
57f888d2d68e39e6d09e5ef0e3d53921fbe42788	in a commutative ring r, one has always	in a commutative ring r, one has always ab – ba = 0. this implies trivially that (b, – a) is a linear relation between a and b. therefore, given a generating set g 1, …, g k {\displaystyle g_{1},\dots,g_{k}} of an ideal i, one calls trivial relation or trivial syzygy every element of the submodule the syzygy module tha...	wikipedia
b2646c41d167157f6d648f0c0aed707a7f203f14	the global dimension of a commutative noetherian ring	the global dimension of a commutative noetherian ring is either infinite, or the minimal n such that every free resolution is finite of length at most n. a commutative noetherian ring is regular if its global dimension is finite. in this case, the global dimension equals its krull dimension. so, hilbert's syzygy theore...	wikipedia
1860d4ab0d2058ec69ddaa338f6841ee3abd798d	a free resolution is finite of length ≤	a free resolution is finite of length ≤ n if s n {\displaystyle s_{n}} is free. in this case, one can take l n = s n, {\displaystyle l_{n}=s_{n},} and l k = 0 {\displaystyle l_{k}=0} (the zero module) for every k > n.	wikipedia
fff63a412c38c5070ee2a22ef725438283fb99c1	for every k ≥ 1, the kernel s	for every k ≥ 1, the kernel s k {\displaystyle s_{k}} of the arrow starting from l k − 1 {\displaystyle l_{k-1}} is a k th syzygy module of m. it follows that the study of free resolutions is the same as the study of syzygy modules.	wikipedia
5e0ce8feec75260d6f9d6a1c8514721eefa80289	where the left arrow is the linear map	where the left arrow is the linear map that maps each g i {\displaystyle g_{i}} to the corresponding g i. {\displaystyle g_{i}.} the kernel of this left arrow is a first syzygy module of m.	wikipedia
70100d849ede1e01eb23a6e22ecddbd0a16dda1b	given a generating set g 1, …, g	given a generating set g 1, …, g n {\displaystyle g_{1},\dots,g_{n}} of an r -module, one can consider a free module of l of basis g 1, …, g n, {\displaystyle g_{1},\dots,g_{n},} where g 1, …, g n {\displaystyle g_{1},\dots,g_{n}} are new indeterminates. this defines an exact sequence	wikipedia
6efb26199a3e07825579f01c960fd8ae67b7324f	theorem — for every positive integer k, the	theorem — for every positive integer k, the k th syzygy module of a given module depends on choices of generating sets, but is unique up to the direct sum with a free module. more precisely, if s 1 {\displaystyle s_{1}} and s 2 {\displaystyle s_{2}} are k th syzygy modules that are obtained by different choices of gene...	wikipedia
09bef183cba3c15693bbc59e5b2a4cfec9d734e9	for obtaining a similar result for higher syzygy	for obtaining a similar result for higher syzygy modules, it remains to prove that, if m is any module, and l is a free module, then m and m ⊕ l have isomorphic syzygy modules. it suffices to consider a generating set of m ⊕ l that consists of a generating set of m and a basis of l. for every relation between the eleme...	wikipedia
88a8f2d6a3b078d365acf1cb1c8323088ec1d676	this proves that the first syzygy module is	this proves that the first syzygy module is "stably unique". more precisely, given two generating sets s 1 {\displaystyle s_{1}} and s 2 {\displaystyle s_{2}} of a module m, if s 1 {\displaystyle s_{1}} and s 2 {\displaystyle s_{2}} are the corresponding modules of relations, then there exist two free modules l 1 {\dis...	wikipedia
05164ecfebb6edd77d1aa4fe26ada3057613e94a	proof. as { x 1, …, x m	proof. as { x 1, …, x m } {\displaystyle \{x_{1},\dots,x_{m}\}} is a generating set, each y i {\displaystyle y_{i}} can be written y i = ∑ α i, j x j. {\displaystyle \textstyle y_{i}=\sum \alpha _{i,j}x_{j}.} this provides a relation r i {\displaystyle r_{i}} between x 1, …, x m, y 1, …, y n. {\displaystyle x_{1},\dots...	wikipedia
1aba4bcc6f431f743c813eca2f0f4cb8a8a84d97	proposition — let { x 1, …, x	proposition — let { x 1, …, x m } {\displaystyle \{x_{1},\dots,x_{m}\}} be a generating set of an r -module m, and y 1, …, y n {\displaystyle y_{1},\dots,y_{n}} be other elements of m. the module of the relations between x 1, …, x m, y 1, …, y n {\displaystyle x_{1},\dots,x_{m},y_{1},\dots,y_{n}} is the direct sum of t...	wikipedia
7f69b3ff90362ded4b721dd4ae3ab9ff4d774d60	generally speaking, in the language of k-theory, a	generally speaking, in the language of k-theory, a property is stable if it becomes true by making a direct sum with a sufficiently large free module. a fundamental property of syzygies modules is that there are "stably independent" of choices of generating sets for involved modules. the following result is the basis o...	wikipedia
5f45ec259ab95da706ee28643cc90f0c061ea12f	if the ring r is noetherian, or, at	if the ring r is noetherian, or, at least coherent, and if m is finitely generated, then the syzygy module is also finitely generated. a syzygy module of this syzygy module is a second syzygy module of m. continuing this way one can define a k th syzygy module for every positive integer k.	wikipedia
faaf3260e1a87552748f6c2528ec523e1ade88e0	if x 1, …, x k {\displaystyle x_{1},\dots,x_{k}}	if x 1, …, x k {\displaystyle x_{1},\dots,x_{k}} is a generating set of m, the relation is often called a syzygy of m. it makes sense to call it a syzygy of m {\displaystyle m} without regard to x 1,.., x k {\displaystyle x_{1},..,x_{k}} because, although the syzygy module depends on the chosen generating set, most of ...	wikipedia
22a30b6820740be4e201925b529707fac484edc6	let r be a ring, and m be	let r be a ring, and m be a left r - module. a linear relation, or simply a relation between k elements x 1, …, x k {\displaystyle x_{1},\dots,x_{k}} of m is a sequence (a 1, …, a k) {\displaystyle (a_{1},\dots,a_{k})} of elements of r such that	wikipedia
c7b42906e3f3c03926a6fa4fe0a9d8e357bb2dfd	if a and b are two elements of	if a and b are two elements of the commutative ring r, then (b, – a) is a relation that is said trivial. the module of trivial relations of an ideal is the submodule of the first syzygy module of the ideal that is generated by the trivial relations between the elements of a generating set of an ideal. the concept of tr...	wikipedia
40bf35cab3f21c3d254e20e64d8cd8bee9d7337b	higher order syzygy modules are defined recursively: a	higher order syzygy modules are defined recursively: a first syzygy module of a module m is simply its syzygy module. for k > 1, a k th syzygy module of m is a syzygy module of a (k – 1) -th syzygy module. hilbert's syzygy theorem states that, if r = k {\displaystyle r=k} is a polynomial ring in n indeterminates over a...	wikipedia
d90827494244331d1e2f0d21e21b0b2941972c08	the relations between e 1, …, e n	the relations between e 1, …, e n {\displaystyle e_{1},\dots,e_{n}} form a module. one is generally interested in the case where e 1, …, e n {\displaystyle e_{1},\dots,e_{n}} is a generating set of a finitely generated module m, in which case the module of the relations is often called a syzygy module of m. the syzygy ...	wikipedia
d5a3cfe044a3ce5e04aa4ff654f941c65a2ff36a	more precisely, if e 1, …, e n	more precisely, if e 1, …, e n {\displaystyle e_{1},\dots,e_{n}} are elements of a (left) module m over a ring r (the case of a vector space over a field is a special case), a relation between e 1, …, e n {\displaystyle e_{1},\dots,e_{n}} is a sequence (f 1, …, f n) {\displaystyle (f_{1},\dots,f_{n})} of elements of r ...	wikipedia