On Baer modules

Jayaram C., Tekir Ü., Koç S.

Revista De La Union Matematica Argentina, vol.63, pp.1-19, 2022 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 63
  • Publication Date: 2022
  • Doi Number: 10.33044/revuma.1741
  • Journal Name: Revista De La Union Matematica Argentina
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET
  • Page Numbers: pp.1-19
  • Marmara University Affiliated: Yes

Abstract

 Recall that a commutative ring R is said to be a Baer ring if for each a ∈ R, ann(a) is generated by an idempotent element b ∈ R. In this paper, we extend the notion of a Baer ring to modules in terms of weak idempotent elements defined in [12]. Let R be a commutative ring with a nonzero identity and M be a unital R-module. M is said to be a Baer module if for each m ∈ M, there exists a weak idempotent element e ∈ R such that annR(m)M = eM. Various examples and properties of Baer modules are given. Also, we characterize certain class of modules/submodules such as von Neumann regular modules/prime submodules in terms of Baer modules.