A note on S-Nakayama’s lemma - Hamed , A. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
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 tS such that tMIM, then (t^′+a)M=0 for some t’S and aI. 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)].