On Principally Quasi-Baer Modules

Abstract

Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally quasi-Baer rings and Baer modules. The mod- ule SM is called principally quasi-Baer if for any m 2 M, lS(Sm) = Se for some e2 = e 2 S. It is proved that (1) if SM is regular and semicommutative module or (2) if MR is principally semisimple and SM is abelian, then SM is a principally quasi-Baer module. The connection between a principally quasi- Baer module SM and polynomial extension, power series extension, Laurent polynomial extension, Laurent power series extension of SM is investigated.