Artinian ring: Difference between revisions

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==Definition for non-commutative rings==
There are two notions:
* [[Left Artinian ring]] must satisfy the descending chain condition on [[left ideal]]s
* [[Right Artinian ring]] must satisfy the descending chain condition on [[right ideal]]s
[[Category: Properties of commutative rings]]

Revision as of 15:31, 30 June 2007

Definition for commutative rings

Symbol-free definition

A commutative unital ring (or more generally a commutative ring) is termed Artinian if it satisfies the descending chain condition on ideals, that is, any descending chain of ideals stabilizes after a finite length.

Definition with symbols

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