Definition:Noetherian Module

Definition
Let $A$ be a commutative ring with unity.

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

Definition 1
$M$ is a Noetherian module every submodule of $M$ is finitely generated.

Definition 2
$M$ is a Noetherian module it satisfies the ascending chain condition on submodules.

Definition 3
$M$ is a Noetherian module it satisfies the maximal condition on submodules.

Also known as
Some sources render the term as noetherian, dropping the capital N.

Also see

 * Equivalence of Definitions of Noetherian Module
 * Definition:Noetherian Ring