On Quasi-Baer and p.q.-Baer Modules
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For an endomorphism α of R, in [1], a module MR is called α-compatible if, for any m 2 M and a 2 R, ma = 0 iff mα(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 α-compatible module MR (1) MR is p.q.-Baer module iff M[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.
Abstract
For an endomorphism α of R, in [1], a module MR is called α-compatible if, for any m 2 M and a 2 R, ma = 0 iff mα(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 α-compatible module MR (1) MR is p.q.-Baer module iff M[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.
참고문헌 (11)
- S. Annin, "Attached Primes Under Skew Polynomial Extensions", ~, Preprint
- M. Ba¸ser, "Reduced and p.q.-Baer Modules", Taiwanese J. Math, 11, pp.257~267 (2007)
- M. Ba¸ser, "On Quasi-Armendariz Modules", Taiwanese J. Math, 12, pp.573~582 (2008)
- G. F. Birkenmeier, "Polynomial extensions of Baer and quasi- Baer rings", J. Pure Appl. Algebra, 159, pp.24~42 (2001)
- G. F. Birkenmeier, "Principally quasi-Baer rings", Comm. Algebra, 29, pp.639~660 (2001)
- G. F. Birkenmeier, "On Polynomial extensions of principally quasi-Baer rings", Kyungpook Math. J, 40, pp.247~253 (2000)
- W. E. Clark, "Twisted matrix units semigroup algebras", Duke Math. J, 34, pp.417~424 (1967)
- Y. Hirano, "On annihilator ideals of a polynomial ring over a noncommutative ring", J. Pure Appl. Algebra, 168, pp.45~52 (2002)
- T. K. Lee, "Reduced Modules, Rings, modules, algebras and abelian groups", Lecture Notes in Pure and Appl. Math, 236, pp.365~377 (2004)
- B. Stenstrom, "Rings of Quotients" (1975), Springer
- H. Tominaga, "On s-unital rings", Math. J. Okoyama Univ, 18, pp.117~134 (1976)