?-endo Baer modules

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

COMMUNICATIONS IN ALGEBRA, vol.48, no.3, pp.1132-1149, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2019.1677690
  • 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.1132-1149
  • Keywords: Baer module, endomorphism rings, projection invariant submodule, quasi-Baer module, pi-extending module, pi-e.Baer module, DIRECT SUMS, INVARIANT, SUBMODULES, RINGS
  • Bursa Uludag University Affiliated: Yes

Abstract

Let N be a submodule of a right R-module M-R, and Then N is said to be projection invariant in M, denoted by if for all We call M-R ?-endo Baer, denoted ?-e.Baer, if for each there exists such that where denotes the left annihilator of N in H. We show that this class of modules lies strictly between the classes of Baer and quasi-Baer modules introduced in 2004 by Rizvi and Roman. Several structural properties are developed. In contrast to the Baer modules of Rizvi and Roman, the free modules of a Baer ring are ?-e.Baer. Moreover, (co-) nonsingularity conditions are introduced which enable us to extend the Chatters-Khuri result (connecting the extending and Baer conditions in a ring) to modules. We provide examples to illustrate and delimit our results.