On normal modules

Jayaram C., TEKİR Ü., KOÇ S., ÇEKEN S.

Communications in Algebra, vol.51, no.4, pp.1479-1491, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1080/00927872.2022.2137519
  • 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.1479-1491
  • Keywords: Baer modules, locally torsion-free modules, normal modules, quasi-regular modules
  • Marmara University Affiliated: Yes

Abstract

Recall that a commutative ring (Formula presented.) is said to be a normal ring if it is reduced and every two distinct minimal prime ideals are comaximal. A finitely generated reduced R-module (Formula presented.) is said to be a normal module if every two distinct minimal prime submodules are comaximal. The concepts of normal modules and locally torsion free modules are different, whereas they are equal in theory of commutative rings. We give many properties and examples of normal modules, we use them to characterize locally torsion free modules and Baer modules. Also, we give the topological characterizations of normal modules.