# Definition:Artinian Module

## Definition

Let $A$ be a commutative ring with unity.

Let $M$ be an $A$-module

Then $M$ is a Artinian module if either of the following conditions hold:

$(1): \quad$ $M$ satisfies the descending chain condition on submodules
$(2): \quad$ $M$ satisfies the minimal condition on submodules.

## Source of Name

This entry was named for Emil Artin.