Category:Definitions/Noetherian Modules
Jump to navigation
Jump to search
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.
Pages in category "Definitions/Noetherian Modules"
The following 5 pages are in this category, out of 5 total.