Artinian may refer to:
Mathematics
*Objects named for Austrian mathematician
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 lar ...
(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 na ...
, a ring which satisfies the descending chain condition on (one-sided) ideals
**
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 ...
, a module which satisfies the descending chain condition on submodules
**
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 simpler ...
, a group which satisfies the descending chain condition on subgroups
People
*
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 film ...
, 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 character ...
(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.Jacobson (2009), p. 142 and 147 These con ...
*
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 conjectu ...
{{Disambiguation, math, surname