Feebly Baer Rings and Modules
Journal
Communications in Algebra
Journal Volume
42
Journal Issue
10
Pages
4281-4295
Date Issued
2014
Author(s)
Abstract
Abstract A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e2 = e ∈ R such that xe = 0 and ea = a. The ring R is called feebly Baer if RR is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [Citation6]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed. Key Words: Feebly Baer ring and moduleVon Neumann regular ringp.p. ring and moduleTriangular matrix ringpolynomial modulesKeywords: 2010 Mathematics Subject ClassificationPrimary 16E50 ACKNOWLEDGMENTS The authors are grateful to the referee for valuable comments and suggestions. Notes Communicated by T. Albn.
Type
journal article