Publication: On S-multiplication modules
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Date
2020
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TAYLOR & FRANCIS INC
Abstract
In this article, we introduce S-multiplication modules which are a generalization of multiplication modules. Let M be an R-module and a multiplicatively closed subset. M is said to be an S-multiplication module if for each submodule N of M there exist and an ideal I of R such that 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
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Keywords
multiplication module, prime submodule, S-multiplication module, S-prime submodule