Nakayama's lemma


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Nakayama's lemma

[‚nä·kä‚yā·mäz ′lem·ə]
(mathematics)
The proposition that, if R is a commutative ring, I is an ideal contained in all maximal ideals of R, and M is a finitely generated module over R, and if IM = M, where IM denotes the set of all elements of the form am with a in I and m in M, then M = 0.