On Quasi-Baer and p.q.-Baer Modules

Abstract

For an endomorphism of R, in (1), a module MR is called -compatible if, for any m 2 M and a 2 R, ma = 0 i m (a) = 0, which are a generalization of -reduced modules. We study on the relationship between the quasi-Baerness and p.q.- Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of (2) and some results in (9). In particular, we show: for an -compatible module MR (1) MR is p.q.-Baer module i M(x; )R(x; ) is p.q.-Baer module. (2) for an automorphism of R, MR is p.q.-Baer module i M(x,x 1 ; )R(x,x 1; ) is p.q.- Baer module.