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Nilpotent elements of skew Hurwitz series rings

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Abstract

For a ring endomorphism \(\alpha \), we consider the problem of determining when an element f of the skew Hurwitz series ring \( (HR, \alpha )\) is nilpotent. As an application, it is shown that the skew Hurwitz series ring \( (HR, \alpha )\) is weak zip (resp. weak symmetric) if and only if R is weak zip (resp. weak symmetric) under some additional conditions. We also characterize when a skew Hurwitz series ring is 2-primal.

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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. Nilpotent elements of skew Hurwitz series rings. Rend. Circ. Mat. Palermo, II. Ser 65, 451–458 (2016). https://doi.org/10.1007/s12215-016-0245-y

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  • DOI: https://doi.org/10.1007/s12215-016-0245-y

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