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Weakly principally quasi-Baer skew generalized power series rings

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Abstract

Let \((S,\le )\) be a strictly totally ordered monoid and R an \((S,\omega )\)-weakly rigid ring, where \(\omega :S\rightarrow End(R)\) is a monoid homomorphism. In this paper, we study the weakly p.q.-Bear property of the skew generalized power series ring \(R[[S,\omega ]]\). As a consequence, the weakly p.q.-Baer property of the skew power series ring \(R[[x;\alpha ]]\) and the skew Laurent power series ring \(R[[x,x^{-1};\alpha ]]\) are determined, where \(\alpha\) is a ring endomorphism of R.

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Acknowledgements

We are thankful to Professor André Leroy and the referees for their valuable comments and suggestions that have greatly improved the presentation of the paper.

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  1. Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

    Ali Majidinya & Ahmad Moussavi

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  1. Ali Majidinya
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  2. Ahmad Moussavi
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Correspondence to Ahmad Moussavi.

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Majidinya, A., Moussavi, A. Weakly principally quasi-Baer skew generalized power series rings. AAECC 32, 409–425 (2021). https://doi.org/10.1007/s00200-021-00499-3

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