Category:Definitions/Artinian Modules

This category contains definitions related to Artinian Modules.
Related results can be found in Category:Artinian Modules.

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.