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Skew polynomial superrings

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

The purpose of this paper is to define the skew polynomial superrings arising from Krasner (hyperfields) hyperrings and study their ideals and some of their properties. In this work, we showed that the skew polynomial superrings are principal superideal superdomains which are not necessarily commutative. We also proved the division theorem for these skew polynomial superrings and provided an algorithm for the decomposition of a polynomial to a product of some irreducible polynomials.

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Acknowledgements

The authors are deeply grateful to the referees for their constructive comments that helped to improve the paper.

Funding

This work is supported by Foundation of Chongqing Municipal Key Laboratory of Institutions of Higher Education ([2017]3), Foundation of Chongqing Development and Reform Commission (2017[1007]) and Foundation of Chongqing Three Gorges University.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing and control, Chongqing Three Gorges University, Chongqing, People’s Republic of China

    Surdive Atamewoue Tsafack & Yuming Feng

  2. School of Computer Science and Engineering, Chongqing Three Gorges University, Wanzhou, Chongqing, 404000, China

    Yuming Feng

  3. Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Yuming Feng

  4. Chongqing Engineering Research Center of Internet of Things and Intelligent Control Technology, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Yuming Feng

  5. School of Three Gorges Artificial Intelligence, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Yuming Feng

  6. Department of Mathematics, University of Yaounde I, 47 Yaounde, Yaoundé, Cameroon

    Surdive Atamewoue Tsafack

  7. Australian AI Institute, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Shiping Wen

  8. Department of Mathematics, University of Ibadan, Ibadan, Nigeria

    Babatunde Oluwaseun Onasanya

Authors
  1. Surdive Atamewoue Tsafack
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  2. Shiping Wen
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  3. Babatunde Oluwaseun Onasanya
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  4. Yuming Feng
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All authors contribute equally to this paper.

Corresponding author

Correspondence to Yuming Feng.

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Atamewoue Tsafack, S., Wen, S., Onasanya, B.O. et al. Skew polynomial superrings. Soft Comput 26, 11277–11286 (2022). https://doi.org/10.1007/s00500-022-07372-6

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  • DOI: https://doi.org/10.1007/s00500-022-07372-6

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