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Characteristic, C-Characteristic and Positive Cones in Hyperfields

Author

Listed:
  • Dawid Edmund Kędzierski

    (Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland)

  • Alessandro Linzi

    (Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

  • Hanna Stojałowska

    (Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland)

Abstract

We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for deciding whether certain hyperfields cannot be obtained via Krasner’s quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for the C-characteristic. Finally, we study the (directed) graph associated with the strict partial order induced by a positive cone in a hyperfield in various examples.

Suggested Citation

  • Dawid Edmund Kędzierski & Alessandro Linzi & Hanna Stojałowska, 2023. "Characteristic, C-Characteristic and Positive Cones in Hyperfields," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:779-:d:1056958
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    References listed on IDEAS

    as
    1. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
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