Definition:Artinian Module
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Definition
Let $A$ be a commutative ring with unity.
Let $M$ be an $A$-module.
Definition 1
$M$ is a Artinian module if and only if:
- $M$ satisfies the descending chain condition.
Definition 2
$M$ is a Artinian module if and only if:
- $M$ satisfies the minimal condition.
Also see
- Results about Artinian modules can be found here.
Source of Name
This entry was named for Emil Artin.
Sources
- 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $6$: Chain Conditions