# Artinian

Artinian
a) (Of a ring) in which any descending chain of ideals eventually starts repeating.
b) (Of a module) in which any descending chain of submodules eventually starts repeating.

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• Artinian — Artine Artinian (* 1908 in Bulgarien; † 19. November 2005 in Palm Beach) war ein US amerikanischer Literaturwissenschaftler und Philanthrop. Leben Artinian wurde 1908 in Bulgarien geboren. Als 13 jähriger Teenager wanderte er über Ellis Island in …   Deutsch Wikipedia

• Artinian — In mathematics, Artinian, named for Emil Artin, is an adjective that describes objects that satisfy particular cases of the descending chain condition.*A ring is an Artinian ring if it satisfies the descending chain condition on ideals. *A module …   Wikipedia

• Artinian module — In abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its 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… …   Wikipedia

• Artinian ring — In abstract algebra, an Artinian ring is a ring that satisfies the descending chain condition on ideals. They are also called Artin rings.There are two classes of rings that have very similar properties:* Rings whose underlying sets are finite. * …   Wikipedia

• Artinian, Artine — ▪ 2006       Bulgarian born American literary scholar (b. Dec. 8, 1907, Pazardzhik, Bulg. d. Nov. 19, 2005, Lantana, Fla.), was a renowned French literature scholar. Artinian translated and edited The Complete Short Stories of Guy de Maupassant… …   Universalium

• Artine Artinian — (* 8. Dezember 1907 in Pasardschik, Bulgarien; † 19. November 2005 in Lantana, Florida) war ein US amerikanischer Literaturwissenschaftler und Philanthrop. Leben Artinian wanderte als 13 jähriger Teenager über Ellis Island in die USA ein und ließ …   Deutsch Wikipedia

• Artine Artinian — (December 8 1907 November 19 2005) was a French literature scholar of Armenian descent, notable for his manuscript collection, who was immortalized as a fictional character by Gore Vidal.cite news|first=New York|last=Times|title=Artine Artinian,… …   Wikipedia

• Araz Artinian — ( hy. Արազ Արթինեան) is a Armenian filmmaker and documentarian. [Araz Artinian s The Genocide in Me The Armenian reporter] She was born Montreal, Quebec.In 1999, she started working with Atom Egoyan as Head Researcher for his feature film Ararat… …   Wikipedia

• Serial module — Chain ring redirects here. For the bicycle part, see Chainring. In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M,… …   Wikipedia

• Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… …   Wikipedia

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