Noetherian module

In ring theory, if R is a ring and M is a module over R, then M is Noetherian if M satisfies the ascending chain condition on its submodules when they are ordered by inclusion.

Noetherian modules are named in honor of Emmy Noether.

Any finitely generated module over a Noetherian ring is a Noetherian module.

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See also: Noetherian module, Ascending chain condition, Emmy Noether, Mathematics, Module (mathematics), Noetherian ring, Ring (mathematics), Ring theory