A note on S-Nakayama’s lemma
Keywords:
Nakayama’s lemma, S-finite, S-w-finiteAbstract
We propose an S-version of Nakayama's lemma. Let R be a commutative ring, S a multiplicative subset of R, and M be an S-finite R-module. Also let I be an ideal of R. We show that if there exists t∈S such that tM⊆IM, then
(t′+a)M=0 for some t′∈S and a∈I. We also give an analog of Nakayama's lemma for a w-ideal and an S-w-finite R-module, where R is an integral domain.
Thus, we generalize the result obtained by Wang and McCasland [Commun. Algebra, 25, 1285–1306 (1997)].
References
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