Π-endo Baer modules. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Birkenmeier, Gary F.; Kara, Yeliz; Tercan, Adnan
• Is Part Of: Communications in algebra. Volume 48:Issue 3(2020)
• Page Start: 1132
• Page End: 1149
• Publication Date: 2020-03-03
• Subjects: Baer module -- endomorphism rings -- projection invariant submodule -- quasi-Baer module -- π-extending module -- π-e.Baer module; Primary: 16D10 -- 16S50 -- Secondary: 16D80; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1677690
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let N be a submodule of a right R -module MR, and H = End ( M R ) . Then N is said to be projection invariant in M, denoted by N ⊴ p M, if e N ⊆ N for all e = e 2 ∈ H . We call MR π-endo Baer, denoted π -e.Baer, if for each N ⊴ p M there exists e = e 2 ∈ H such that l H ( N ) = H e where l H ( N ) 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 π -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.