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Principally quasi-Baer skew Hurwitz series rings

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Abstract

A ring is quasi-Baer (respectively, right p.q.-Baer) in case the right annihilator of every (respectively, principal right) ideal is generated by an idempotent, as a right ideal. A ring R is right AIP if the right annihilator of any right ideal of R is pure as a right ideal. In this article, we study relations between the quasi-Baer, right p.q.-Baer, and right AIP properties of a ring R, and its skew Hurwitz series ring \((HR, \alpha )\), where R is a ring equipped with an endomorphism \(\alpha \). Examples to illustrate and delimit the theory are provided.

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Acknowledgments

The author would like to express their deep gratitude to the referee for a very careful reading of the article, and many valuable comments, which have greatly improved the presentation of the article.

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  1. Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    Kamal Paykan

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  1. Kamal Paykan
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Correspondence to Kamal Paykan.

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Paykan, K. Principally quasi-Baer skew Hurwitz series rings. Boll Unione Mat Ital 10, 607–616 (2017). https://doi.org/10.1007/s40574-016-0098-5

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  • DOI: https://doi.org/10.1007/s40574-016-0098-5

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