On S-comultiplication modules

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Yıldız E., Tekir Ü., Koç S.

TURKISH JOURNAL OF MATHEMATICS, vol.46, no.SI-2, pp.2034-2046, 2022 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 46 Issue: SI-2
  • Publication Date: 2022
  • Doi Number: 10.55730/1300-0098.3251
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2034-2046

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. 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.