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 a $p.p.$-module iff $M_R$ 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.