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List Of Things Named After Emil Artin
{{Short description, none These are things named after Emil Artin, a mathematician. * Ankeny–Artin–Chowla congruence * Artin algebra * Artin billiards * Artin braid group * Artin character * Artin conductor * Artin's conjecture for conjectures by Artin. These include :* Artin's conjecture on primitive roots :* Artin conjecture on L-functions * Artin group * Artin–Hasse exponential * Artin L-function * Artin reciprocity * Artin–Rees lemma * Artin representation * Artin–Schreier theorem * Artin–Schreier theory * Artin's theorem on induced characters * Artin–Zorn theorem * Artinian ideal * Artinian module * Artinian ring * Artin–Tate lemma * Artin–Tits group * Fox–Artin arc * Wedderburn–Artin theorem * Emil Artin Junior Prize in Mathematics See also * Artinian Artin Artin may refer to: * Artin (name), a surname and given name, including a list of people with the name ** Artin, a variant of Harutyun Harutyun ( hy, Հարություն and in Western ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Along with Emmy Noether, he is considered the founder of modern abstract algebra. Early life and education Parents Emil Artin was born in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of mixed Austrian and Armenian descent. His Armenian last name was Artinian which was shortened to Artin. Several documents, including Emil's birth certificate, list the father's occupation as “opera singer” though others list it as “art dealer.” It seems at least plausible that he and Emma had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin Representation
In mathematics, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by as an expression appearing in the functional equation of an Artin L-function. Local Artin conductors Suppose that ''L'' is a finite Galois extension of the local field ''K'', with Galois group ''G''. If \chi is a character of ''G'', then the Artin conductor of \chi is the number :f(\chi)=\sum_\frac(\chi(1)-\chi(G_i)) where ''G''''i'' is the ''i''-th ramification group (in lower numbering), of order ''g''''i'', and χ(''G''''i'') is the average value of \chi on ''G''''i''.Serre (1967) p.158 By a result of Artin, the local conductor is an integer.Serre (1967) p.159 Heuristically, the Artin conductor measures how far the action of the higher ramification groups is from being trivial. In particular, if χ is unramified, then its Artin conductor is zero. Thus if ''L'' is unramified over ''K'', then the Artin conductors of all χ are zero. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Artin Junior Prize In Mathematics
Established in 2001, the Emil Artin Junior Prize in Mathematics is presented usually every year to a former student of an Armenian university, who is under the age of thirty-five, for outstanding contributions in algebra, geometry, topology, and number theory. The award is announced in the Notices of the American Mathematical Society. The prize is named after Emil Artin, who was of Armenian descent. Although eligibility for the prize is not fully international, as the recipient has to have studied in Armenia, awards are made only for specific outstanding publications in leading international journals. Recipient of the Emil Artin Junior Prize *2001 Vahagn Mikaelian *2002 Artur Barkhudaryan *2004 Gurgen R. Asatryan *2005 Mihran Papikian *2007 Ashot Minasyan *2008 Nansen Petrosyan *2009 Grigor Sargsyan *2010 Hrant Hakobyan *2011 Lilya Budaghyan *2014 Sevak Mkrtchyan *2015 Anush Tserunyan *2016 Lilit Martirosyan *2018 Davit Harutyunyan *2019 Vahagn Aslanyan *2020 Levon Haykazyan *202 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wedderburn–Artin Theorem
In algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that an (Artinian) semisimple ring ''R'' is isomorphic to a product of finitely many -by- matrix rings over division rings , for some integers , both of which are uniquely determined up to permutation of the index . In particular, any simple left or right Artinian ring is isomorphic to an ''n''-by-''n'' matrix ring over a division ring ''D'', where both ''n'' and ''D'' are uniquely determined. Theorem Let be a (Artinian) semisimple ring. Then the Wedderburn–Artin theorem states that is isomorphic to a product of finitely many -by- matrix rings M_(D_i) over division rings , for some integers , both of which are uniquely determined up to permutation of the index . There is also a version of the Wedderburn–Artin theorem for algebras over a field . If is a finite-dimensional semisimple -algebra, then each in the above statement is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wild Arc
In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment. found the first example of a wild arc, and found another example called the Fox-Artin arc whose complement is not simply connected. See also *Wild knot *Horned sphere The Alexander horned sphere is a pathological object in topology discovered by . Construction The Alexander horned sphere is the particular embedding of a sphere in 3-dimensional Euclidean space obtained by the following construction, starting ... Further reading * * * * * {{Topology Geometric topology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin–Tits Group
In the mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete group (mathematics), groups defined by simple presentation of a group, presentations. They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named after Emil Artin, due to his early work on braid groups in the 1920s to 1940s, and Jacques Tits who developed the theory of a more general class of groups in the 1960s. Definition An Artin–Tits presentation is a group presentation of a group, presentation \langle S \mid R \rangle where S is a (usually finite) set of generators and R is a set of Artin–Tits relations, namely relations of the form stst\ldots = tsts\ldots for distinct s, t in S, where both sides have equal lengths, and there exists at most one relation for each pair of distinct generators ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin–Tate Lemma
In algebra, the Artin–Tate lemma, named after Emil Artin and John Tate, states: :Let ''A'' be a commutative Noetherian ring and B \sub C commutative algebras over ''A''. If ''C'' is of finite type over ''A'' and if ''C'' is finite over ''B'', then ''B'' is of finite type over ''A''. (Here, "of finite type" means "finitely generated algebra" and "finite" means "finitely generated module".) The lemma was introduced by E. Artin and J. Tate in 1951 to give a proof of Hilbert's Nullstellensatz. The lemma is similar to the Eakin–Nagata theorem, which says: if ''C'' is finite over ''B'' and ''C'' is a Noetherian ring, then ''B'' is a Noetherian ring. Proof The following proof can be found in Atiyah–MacDonald. M. Atiyah, I.G. Macdonald, ''Introduction to Commutative Algebra'', Addison–Wesley, 1994. . Proposition 7.8 Let x_1,\ldots, x_m generate C as an A-algebra and let y_1, \ldots, y_n generate C as a B-module. Then we can write :x_i = \sum_j b_y_j \quad \text \quad y_iy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artinian Ring
In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously generalizes finite rings and rings that are finite-dimensional vector spaces over fields. The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition. Precisely, a ring is left Artinian if it satisfies the descending chain condition on left ideals, right Artinian if it satisfies the descending chain condition on right ideals, and Artinian or two-sided Artinian if it is both left and right Artinian. For commutative rings the left and right definitions coincide, but in general they are distinct from each other. The Artin–Wedderburn theorem charact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artinian Module
In mathematics, specifically abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over itself (with left or right multiplication). Both concepts are named for Emil Artin. In the presence of the axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collectio ..., the descending chain condition becomes equivalent to the minimum condition, and so that may be used in the definition instead. Like Noetherian modules, Artinian modules enjoy the following heredity property: * If ''M'' is an Artinian ''R''-module, then so is any submodule and any quotient module, quotient of ''M''. The converse (logic), co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artinian Ideal
In abstract algebra, an Artinian ideal, named after Emil Artin, is encountered in ring theory, in particular, with polynomial rings. Given a polynomial ring ''R'' = ''k'' 'X''1, ... ''X''''n''where ''k'' is some field, an Artinian ideal is an ideal ''I'' in ''R'' for which the Krull dimension In commutative algebra, the Krull dimension of a commutative ring ''R'', named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally t ... of the quotient ring ''R''/''I'' is 0. Also, less precisely, one can think of an Artinian ideal as one that has at least each indeterminate in ''R'' raised to a power greater than 0 as a generator. If an ideal is not Artinian, one can take the Artinian closure of it as follows. First, take the least common multiple of the generators of the ideal. Second, add to the generating set of the ideal each indeterminate of the LCM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin–Zorn Theorem
In mathematics, the Artin–Zorn theorem, named after Emil Artin and Max Zorn, states that any finite alternative division ring is necessarily a finite field. It was first published in 1930 by Zorn, but in his publication Zorn credited it to Artin. The Artin–Zorn theorem is a generalization of the Wedderburn theorem, which states that finite associative division rings are fields. As a geometric consequence, every finite Moufang plane In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation plane is a projective plane that has a ''translation line'', that is, a line with the proper ... is the classical projective plane over a finite field.. References Theorems in ring theory {{Abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin's Theorem On Induced Characters
In representation theory, a branch of mathematics, Artin's theorem, introduced by E. Artin, states that a character on a finite group is a rational linear combination of characters induced from cyclic subgroups of the group. There is a similar but somehow more precise theorem due to Brauer, which says that the theorem remains true if "rational" and "cyclic subgroup" are replaced with "integer" and "elementary subgroup". Proof References *{{cite book , first = Jean-Pierre , last = Serre , author-link = Jean-Pierre Serre , title = Linear Representations of Finite Groups , url = https://archive.org/details/linearrepresenta1977serr , url-access = registration , series = Graduate Texts in Mathematics, 42 , publisher = Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |