Principally Quasi-Baer Skew Power Series Modules |
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Authors: | R. Manaviyat M. Habibi |
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Affiliation: | Department of Pure Mathematics, Faculty of Mathematical Sciences , Tarbiat Modares University , Tehran , Iran |
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Abstract: | A module M R is called principally quasi-Baer (or simply p.q.-Baer) if the annihilator of every cyclic submodule of M R is generated by an idempotent, as a right ideal. Let α be an automorphism of R and M R be an α-compatible module and every countable subset of right semicentral idempotents in R has a generalized countable join or R satisfies the ACC on left annihilator ideals. It is shown that M R is p.q.-Baer if and only if M[[x]] R[[x; α]] is p.q.-Baer if and only if M[[x, x ?1]] R[[x, x ?1; α]] is p.q.-Baer. As a consequence, we unify and extend nontrivially many of the previously known results such as [11 Hashemi , E. ( 2008 ). A note on p.q.-Baer modules . New York J. Math. 14 : 403 – 410 . [Google Scholar], 15 Huang , F. K. ( 2008 ). A note on extensions of principally quasi-Baer rings . Taiwan. J. Math. 45 ( 4 ): 469 – 481 . [Google Scholar], 20 Liu , Z. ( 2002 ). A note on principally quasi-Baer rings . Comm. Algebra 30 ( 8 ): 3885 – 3890 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. Examples to illustrate and delimit the theory are provided. |
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Keywords: | Polynomial modules Principally quasi-Baer modules Quasi-Baer modules Skew power series modules Skew Laurent series modules |
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