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

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BAŞER M., Harmanci A.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.49, no.2, pp.255-263, 2009 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.5666/kmj.2009.49.2.255
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.255-263
  • Hacettepe University Affiliated: Yes

Abstract

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