Definition:Noetherian Module/Definition 1

Definition

Let $A$ be a commutative ring with unity.

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

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

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