# Category:Noetherian Modules

This category contains results about Noetherian Modules.
Definitions specific to this category can be found in Definitions/Noetherian Modules.

Let $A$ be a commutative ring with unity.

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

### Definition 1

$M$ is a Noetherian module if and only if every submodule of $M$ is finitely generated.

### Definition 2

$M$ is a Noetherian module if and only if it satisfies the ascending chain condition on submodules.

### Definition 3

$M$ is a Noetherian module if and only if it satisfies the maximal condition on submodules.

## Pages in category "Noetherian Modules"

The following 2 pages are in this category, out of 2 total.