Amodule is Noetherian if it obeys theascending chain condition with respect to inclusion, i.e., if every set of increasing sequences ofsubmodules eventually becomes constant.

If amodule is Noetherian, then the following are equivalent.

1. satisfies theascending chain condition onsubmodules.

2. Everysubmodule of isfinitely generated.

3. Every set ofsubmodules of contains amaximal element.

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Cite this as:

Weisstein, Eric W. "Noetherian Module."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NoetherianModule.html

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