The Schroder-Bernstein problem for dual F-Baer modules

KESKİN TÜTÜNCÜ D.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.21, no.07, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 07
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498822501316
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Dual Baer module, dual F-Baer module, preradical
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we introduce dual F-Baer modules and give a characterization of them. Let M be a module and F a fully invariant submodule of M. M is called dual F-Baer if for every family of endomorphisms {g(alpha)}(alpha is an element of I) of M, Sigma(alpha is an element of I) g(alpha)(F) is a direct summand of M. We prove that M is dual F-Baer if and only if M = F circle plus N for some submodule N of M with F dual Baer. We obtain a positive solution for the Schroder-Bernstein problem for certain dual F-Baer modules.