On S-multiplication modules

Anderson D. D., Arabaci T., TEKİR Ü., KOÇ S.

COMMUNICATIONS IN ALGEBRA, vol.48, no.8, pp.3398-3407, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 8
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1737873
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3398-3407
  • Keywords: multiplication module, prime submodule, S-multiplication module, S-prime submodule
  • Marmara University Affiliated: Yes

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