S-principal ideal multiplication modules

ASLANKARAYİĞİT UĞURLU E., KOÇ S., TEKİR Ü.

Communications in Algebra, vol.51, no.6, pp.2510-2519, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.1080/00927872.2022.2164772
  • 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.2510-2519
  • Keywords: PI-multiplication module, S-cyclic module, S-multiplication module, S-Noetherian module, S-prime submodule
  • Marmara University Affiliated: Yes

Abstract

In this paper, we study S-Principal ideal multiplication modules. Let (Formula presented.) be a commutative ring with (Formula presented.) a multiplicatively closed set and (Formula presented.) an A-module. A submodule N of M is said to be an S-multiple of M if there exist (Formula presented.) and a principal ideal I of A such that (Formula presented.). (Formula presented.) is said to be an S-principal ideal multiplication module if every submodule (Formula presented.) of (Formula presented.) is an S-multiple of M. Various examples and properties of S-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extension (Formula presented.) is an (Formula presented.) -principal ideal ring. Also, we prove Cohen type theorem for S-principal ideal multiplication modules in terms of S-prime submodules.