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.