Definition:Noetherian Module/Definition 2

Definition

Let $A$ be a commutative ring with unity.

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

$M$ is a Noetherian module if and only if it satisfies the ascending chain 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

• Results about Noetherian modules can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Noetherian module