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On Non-Commutative Multi-Rings with Involution

Author

Listed:
  • Kaique M. A. Roberto

    (Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, São Paulo 05508-090, Brazil
    The authors contributed equally to this work.)

  • Kaique R. P. Santos

    (Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, São Paulo 05508-090, Brazil
    The authors contributed equally to this work.)

  • Hugo Luiz Mariano

    (Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, São Paulo 05508-090, Brazil
    The authors contributed equally to this work.)

Abstract

The primary motivation for this work is to develop the concept of Marshall’s quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall’s seminal paper. We define two multiplicative properties to address the involutive case and characterize their Marshall quotient. Moreover, this article presents various cases demonstrating that the “multi” version of rings with involution offers many examples, applications, and relatives in (multi)algebraic structures. Therefore, we established the first steps toward the development of an expansion of real algebra and real algebraic geometry to a non-commutative and involutive setting.

Suggested Citation

  • Kaique M. A. Roberto & Kaique R. P. Santos & Hugo Luiz Mariano, 2024. "On Non-Commutative Multi-Rings with Involution," Mathematics, MDPI, vol. 12(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2931-:d:1482145
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    References listed on IDEAS

    as
    1. Anastase Nakassis, 1988. "Recent results in hyperring and hyperfield theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-12, January.
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