On S-comultiplication Modules


Yıldız E., Tekir Ü. , Koç S.

Turkish Journal Of Mathematics, vol.45, pp.1-13, 2021 (Journal Indexed in SCI Expanded)

  • Publication Type: Article / Article
  • Volume: 45
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2107-33
  • Title of Journal : Turkish Journal Of Mathematics
  • Page Numbers: pp.1-13

Abstract

Let R be a commutative ring with 1 ̸= 0 and M be an R-module. Suppose that S ⊆ 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. def i ned 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.