Definition:Artinian Module/Definition 1

Definition

Let $A$ be a commutative ring with unity.

Let $M$ be an $A$-module.

$M$ is a Artinian module if and only if:

$M$ satisfies the descending chain condition.

Sources

• 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $6$: Chain Conditions