KYUNGPOOK Math. J. 49(2009), 255-263 On Quasi-Baer and p.q.-Baer Modules

Abstract. For an endomorphism α of R, in [1], a module MR is called α-compatible if, for any m ∈ M and a ∈ R, ma = 0 iff mα(a) = 0, which are a generalization of α-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 α-compatible moduleMR (1)MR is p.q.-Baer module iffM [x;α]R[x;α] is p.q.-Baer module. (2) for an automorphism α of R, MR is p.q.-Baer module iff M [x, x −1;α]R[x,x−1;α] is p.q.-Baer module. 1