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 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.

Also known as

Some sources render the term Noetherian module as noetherian, dropping the capital N.

Also see

• Equivalence of Definitions of Noetherian Module
• Short Exact Sequence Condition of Noetherian Modules
• Definition:Noetherian Ring

• Results about Noetherian modules can be found here.

Source of Name

This entry was named for Emmy Noether.