Quasi-s.Baer and related modules


Birkenmeier G. F., KARA ŞEN Y., TERCAN A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.21, no.03, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 03
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498822500517
  • 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: Baer module, quasi-Baer module, projection invariant submodule, FI-extending module, pi-extending module, endomorphism ring, BAER, RINGS
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, the s.Baer module concept and some of its generalizations (e.g. quasi-s.Baer, pi-s.Baer and p.q.-s.Baer) are developed. To this end, we characterize the class of rings for which every module is quasi-s.Baer as the class of rings which are finite direct sums of simple rings. Connections are made between the s.Baer (quasi-s.Baer, pi-s.Baer) and the extending (FI-extending, pi-extending) properties. We introduce the notions of quasi-nonsingularity (FI-s.nonsingular, pi-s.nonsingular) and M-cononsingular (FI-M-cononsingular, pi-M-cononsingular) to extend the Chatters-Khuri theorem from rings to modules satisfying s.Baer or related conditions. Moreover, we investigate the transfer of various Baer properties between a module and its ring of scalars. Conditions are found for which some classes of quasi-s.Baer modules coincide with some classes of p.q.-s.Baer modules. Further we show that the class of quasi-s.Baer (p.q.-s.Baer) modules is closed with respect to submodules, extensions, and finite (arbitrary) direct sums. Examples illustrate and delimit our results.