Reduced and P.Q.-Baer Modules

Abstract

In this paper, we study p.q.-Baer modules and some polynomial extensions of p.q.-Baer modules. In particular, we show: (1) For a reduced module M-R,M-R is ap.p.-moduleiff M-R is a p.q.-Baer module. (2) If M-R is an alpha-reduced module where alpha is an endomorphism of R, then M-R is a p.q.-Baer module iff M[x; alpha](R[x;alpha]) is a p.q.-Baer module. (3) For an arbitrary module M-R, M-R is a p.q.-Baer module if and only if M[x](R[x]) is a p.q.-Baer module.