A note on $S$-Nakayama’s lemma

• Date: 2020
• Main Author: Hamed , A.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2332
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $t\in S$ such that $tM\subseteq IM,$ then$(t^\prime+a)M=0$ for some $t&#03...