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], Turk. J. Math. (2019)) 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],Comm. Alg. (2020)), 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.