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Derived Hyperstructures from Hyperconics

Author

Listed:
  • Vahid Vahedi

    (Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran)

  • Morteza Jafarpour

    (Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
    The corresponding author in deep gratitude dedicates this work and gives special thanks to Cardiovascular Surgeon A. R. Alizadeh Ghavidel.)

  • Sarka Hoskova-Mayerova

    (Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic)

  • Hossein Aghabozorgi

    (Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran)

  • Violeta Leoreanu-Fotea

    (Department of Mathematics, Al. I. Cuza University, 6600 Iashi, Romania)

  • Svajone Bekesiene

    (Departament of Defence Technologies, The General Jonas Žemaitis Military Academy of Lithuania, Silo g.5, 10322 Vilnius, Lithuania)

Abstract

In this paper, we introduce generalized quadratic forms and hyperconics over quotient hyperfields as a generalization of the notion of conics on fields. Conic curves utilized in cryptosystems; in fact the public key cryptosystem is based on the digital signature schemes (DLP) in conic curve groups. We associate some hyperoperations to hyperconics and investigate their properties. At the end, a collection of canonical hypergroups connected to hyperconics is proposed.

Suggested Citation

  • Vahid Vahedi & Morteza Jafarpour & Sarka Hoskova-Mayerova & Hossein Aghabozorgi & Violeta Leoreanu-Fotea & Svajone Bekesiene, 2020. "Derived Hyperstructures from Hyperconics," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:429-:d:333210
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    Citations

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    Cited by:

    1. 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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