Principally Quasi-Baer skew Generalized Power Series modules |
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Authors: | A. Majidinya |
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Affiliation: | Department of Pure Mathematics, Faculty of Mathematical Sciences , Tarbiat Modares University , Tehran , Iran |
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Abstract: | Let R be a ring and S a strictly totally ordered monoid. Let ω: S → End(R) be a monoid homomorphism. Let M R be an ω-compatible module and either R satisfies the ascending chain conditions (ACC) on left annihilator ideals or every S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join. We show that M R is p.q.-Baer if and only if the generalized power series module M[[S]] R[[S, ω]] is p.q.-Baer. As a consequence, we deduce that for an ω-compatible ring R, the skew generalized power series ring R[[S, ω]] is right p.q.-Baer if and only if R is right p.q.-Baer and either R satisfies the ACC on left annihilator ideals or any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R. Examples to illustrate and delimit the theory are provided. |
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Keywords: | Generalized power series module Principally quasi-Baer ring Skew generalized power series ring Strictly ordered monoid |
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