Definition:Artinian Module

From ProofWiki
Jump to navigation Jump to search

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