Artinian may refer to:
Mathematics
*Objects named for Austrian mathematician
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, Armenian descent.
Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number t ...
(1898–1962)
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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 Arti ...
, an ideal ''I'' in ''R'' for which the Krull dimension of the quotient ring ''R/I'' is 0
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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 ...
, a ring which satisfies the descending chain condition on (one-sided) ideals
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Artinian module Artinian may refer to:
Mathematics
*Objects named for Austrian mathematician Emil Artin (1898–1962)
**Artinian ideal, an ideal ''I'' in ''R'' for which the Krull dimension of the quotient ring ''R/I'' is 0
**Artinian ring, a ring which satisfies ...
, a module which satisfies the descending chain condition on submodules
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Artinian group
In mathematics, specifically group theory, a subgroup series of a group G is a chain of subgroups:
:1 = A_0 \leq A_1 \leq \cdots \leq A_n = G
where 1 is the trivial subgroup. Subgroup series can simplify the study of a group to the study of simpl ...
, a group which satisfies the descending chain condition on subgroups
People
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Araz Artinian
Araz Artinian is a Canadian filmmaker and documentarian of Armenian descent.Araz Artinian's "The Genocide" - The Armenian reporter She was born Montreal, Quebec.
In 1999, she started working with Atom Egoyan as Head Researcher for his feature fil ...
, Armenian-Canadian filmmaker and photographer
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Artine Artinian
Artine Artinian (December 8, 1907 – November 19, 2005) was a distinguished French literature scholar of Armenian descent, notable for his valuable collection of French literary manuscripts and artwork. He was immortalized as a fictional charact ...
(1907–2005), French literature scholar
See also
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Descending chain condition
In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly ideals in certain commutative rings. These conditions played an important r ...
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List of things named after Emil Artin
{{Disambiguation, math, surname