Further results on skew Hurwitz series ring (I)

Abstract

In this paper, we continue the study of skew Hurwitz series ring \((H R, \alpha )\), where R is a ring equipped with an endomorphism \(\alpha \). In particular, we investigate the problem when a skew Hurwitz series series ring \((HR, \alpha )\) has the same Goldie rank as the ring R, and we obtain partial characterizations for it to be serial semiprime. Finally, we will obtain criterion for skew Hurwitz series rings to be right non-singular.

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Acknowledgements

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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Correspondence to Kamal Paykan.

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Paykan, K. Further results on skew Hurwitz series ring (I). Rend. Circ. Mat. Palermo, II. Ser 69, 1251–1258 (2020). https://doi.org/10.1007/s12215-019-00470-9

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Keywords

  • Skew Hurwitz series ring
  • Goldie rank
  • Serial semiprime ring
  • Non-singular

Mathematics Subject Classification

  • 16S99
  • 16W60
  • 16S36
  • 16N40