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Superring of Polynomials over a Hyperring

Author

Listed:
  • Reza Ameri

    (School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran 79416-55665, Iran
    These authors contributed equally to this work.)

  • Mansour Eyvazi

    (School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran 79416-55665, Iran
    These authors contributed equally to this work.)

  • Sarka Hoskova-Mayerova

    (Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic
    These authors contributed equally to this work.)

Abstract

A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.

Suggested Citation

  • Reza Ameri & Mansour Eyvazi & Sarka Hoskova-Mayerova, 2019. "Superring of Polynomials over a Hyperring," Mathematics, MDPI, vol. 7(10), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:902-:d:271160
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    References listed on IDEAS

    as
    1. Marc Krasner, 1983. "A class of hyperrings and hyperfields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-5, January.
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    Cited by:

    1. Ergül Türkmen & Burcu Nişancı Türkmen & Öznur Kulak, 2023. "Spectrum of Zariski Topology in Multiplication Krasner Hypermodules," Mathematics, MDPI, vol. 11(7), pages 1-10, April.
    2. Christos G. Massouros & Gerasimos G. Massouros, 2023. "On the Borderline of Fields and Hyperfields," Mathematics, MDPI, vol. 11(6), pages 1-35, March.

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