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artinian (Definition)

A module $M$ is artinian if it satisfies the following equivalent conditions:

A ring $R$ is left artinian if it is artinian as a left module over itself (i.e. if $_RR$ is an artinian module), and right artinian if it is artinian as a right module over itself (i.e. if $R_R$ is an artinian module), and simply artinian if both conditions hold.




"artinian" is owned by antizeus.
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See Also: noetherian ring, noetherian, hollow matrix rings

Other names:  left artinian, right artinian

Attachments:
an Artinian integral domain is a field (Theorem) by yark
example of an Artinian module which is not Noetherian (Example) by joking
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Cross-references: left module, ring, minimal element, submodules, descending chain condition, equivalent, module
There are 16 references to this entry.

This is version 3 of artinian, born on 2002-02-24, modified 2003-09-20.
Object id is 2566, canonical name is Artinian.
Accessed 6463 times total.

Classification:
AMS MSC16D10 (Associative rings and algebras :: Modules, bimodules and ideals :: General module theory)

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