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Recent results in hyperring and hyperfield theory

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  • Anastase Nakassis

Abstract

This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the sum of two elements is a subset of the structure. The results in this paper show that these structures cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and hyperrings cannot be derived from the corresponding results in field and ring theory.

Suggested Citation

  • Anastase Nakassis, 1988. "Recent results in hyperring and hyperfield theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:825185
    DOI: 10.1155/S0161171288000250
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    Cited by:

    1. Hashem Bordbar & Irina Cristea, 2021. "Regular Parameter Elements and Regular Local Hyperrings," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    2. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    3. 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.
    4. Christos G. Massouros & Gerasimos G. Massouros, 2023. "On the Borderline of Fields and Hyperfields," Mathematics, MDPI, vol. 11(6), pages 1-35, March.
    5. Gerasimos Massouros & Christos Massouros, 2020. "Hypercompositional Algebra, Computer Science and Geometry," Mathematics, MDPI, vol. 8(8), pages 1-33, August.

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