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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nakayama's lemma for half-exact functors

Authors: Arthur Ogus and George Bergman
Journal: Proc. Amer. Math. Soc. 31 (1972), 67-74
MSC: Primary 13D99
MathSciNet review: 0302633
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Abstract: We prove an analog of Nakayama's Lemma, in which the finitely generated module is replaced by a half-exact functor from modules to modules. As applications, we obtain simple proofs of Grothendieck's ``property of exchange'' for a sheaf of modules under base change, and of the ``local criterion for flatness."

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Keywords: Nakayama's Lemma, half-exact functor, additive category with $ R$-linear structure, base change, tensor product, cohomological $ \delta $-functor, property of exchange, flat module
Article copyright: © Copyright 1972 American Mathematical Society

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