On S-comultiplication modules

Abstract

Let R be a commutative ring with 1 not equal 0 and M be an R-module. Suppose that S subset of R is a multiplicatively closed set of R. Recently Sevim et al. in [19] introduced the notion of an S-prime submodule which is a generalization of a prime submodule and used them to characterize certain classes of rings/modules such as prime submodules, simple modules, torsion free modules, S-Noetherian modules and etc. Afterwards, in [2], Anderson et al. defined the concepts of S-multiplication modules and S-cyclic modules which are S-versions of multiplication and cyclic modules and extended many results on multiplication and cyclic modules to S-multiplication and S-cyclic modules. Here, in this article, we introduce and study S-comultiplication modules which are the dual notion of S-multiplication module. We also characterize certain classes of rings/modules such as comultiplication modules, S-second submodules, S-prime ideals and S-cyclic modules in terms of S-comultiplication modules. Moreover, we prove S-version of the dual Nakayama's Lemma.