On S-multiplication modules

Abstract

In this article, we introduce S-multiplication modules which are a generalization of multiplication modules. Let M be an R-module and $S\subseteq R$ a multiplicatively closed subset. M is said to be an S-multiplication module if for each submodule N of M there exist $s\in S$ and an ideal I of R such that $sN\subseteq IM\subseteq N.$ Besides giving many properties of S-multiplication modules, we generalize some results on multiplication modules to S-multiplication modules. Also, we study S-prime submodules in S-multiplication modules. In particular, we generalize prime avoidance lemma for multiplication modules to S -multiplication modules. Furthermore, we characterize multiplication modules in terms of S-multiplication modules.

Communicated by Toma Albu

Keywords:

• multiplication module
• prime submodule
• S-multiplication module
• S-prime submodule

2010 Mathematics Subject Classification:

• 16P40
• 13A15

View correction statement:

Correction to: On S-multiplication modules

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.