# Definition:Artinian Module

## 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.