Category:Definitions/Noetherian Modules

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This category contains definitions related to Noetherian Modules.
Related results can be found in Category: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.