Nakayama's lemma

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Nakayama's lemma [‚nä·kä‚yā·mäz ′lem·ə]

(mathematics)

The proposition that, ifRis a commutative ring,Iis an ideal contained in all maximal ideals ofR, andMis a finitely generated module overR, and ifIM=M, whereIMdenotes the set of all elements of the formamwithainIandminM, thenM= 0.

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