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searching for Noetherian module 4 found (23 total)

Noncommutative ring (2,804 words) [view diff] exact match in snippet view article find links to article

Naturally, if U is a Noetherian module, this holds. If R is Noetherian, and U is finitely generated, then U is a Noetherian module over R, and the conclusion

Nakayama's lemma (3,604 words) [view diff] exact match in snippet view article find links to article

Naturally, if U is a Noetherian module, this holds. If R is Noetherian, and U is finitely generated, then U is a Noetherian module over R, and the conclusion

Artin–Rees lemma (1,367 words) [view diff] exact match in snippet view article find links to article

called the Rees algebra.) Thus, B I M {\displaystyle B_{I}M} is a Noetherian module and any submodule is finitely generated over B I R {\displaystyle

Primary decomposition (4,366 words) [view diff] exact match in snippet view article find links to article

since zero is in it). The set has a maximal element Q since M is a Noetherian module. If Q is not P-primary, say, P ′ ≠ P {\displaystyle P'\neq P} is associated