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In this article, we introduce S-multiplication modules which are a generalization of multiplication modules. Let M be an R-module and S⊆R a multiplicatively closed subset. M is said to be an S-multiplication module if for each submodule N of M there exist s∈S and an ideal I of R such that sN⊆IM⊆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.
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Anderson et al. (2020) studied this question.
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