Locally torsion-free modules

Jayaram C., Uǧurlu E. A. , Tekir Ü., Koç S.

Journal of Algebra and its Applications, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498823501037
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Baer modules, Baer rings, locally integral domains, locally torsion-free modules, normal modules, quasi-regular modules, quasi-regular rings, torsion-free modules, von Neumann regular modules, von Neumann regular rings

Abstract

© 2023 World Scientific Publishing Company.Recall that a commutative ring R is a locally integral domain if its localization RP is an integral domain for each prime ideal P of R. Our aim in this paper is to extend the notion of locally integral domains to modules. Let R be a commutative ring with a unity and M a nonzero unital R-module. M is called a locally torsion-free module if the localization MP of M is a torsion-free RP-module for each prime ideal P of R. In addition to giving many properties of locally torsion-free modules, we use them to characterize Baer modules, torsion free modules, and von Neumann regular rings.