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Open AccessArticle

Derived Hyperstructures from Hyperconics

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Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
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Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic
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Department of Mathematics, Al. I. Cuza University, 6600 Iashi, Romania
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Departament of Defence Technologies, The General Jonas Žemaitis Military Academy of Lithuania, Silo g.5, 10322 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
The corresponding author in deep gratitude dedicates this work and gives special thanks to Cardiovascular Surgeon A. R. Alizadeh Ghavidel.
Mathematics 2020, 8(3), 429; https://doi.org/10.3390/math8030429
Received: 26 January 2020 / Revised: 7 March 2020 / Accepted: 11 March 2020 / Published: 16 March 2020
(This article belongs to the Special Issue Hypercompositional Algebra and Applications)
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. View Full-Text
Keywords: hypergroup; hyperring; hyperfield; (hyper)conics; quadratic forms hypergroup; hyperring; hyperfield; (hyper)conics; quadratic forms
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Vahedi, V.; Jafarpour, M.; Hoskova-Mayerova, S.; Aghabozorgi, H.; Leoreanu-Fotea, V.; Bekesiene, S. Derived Hyperstructures from Hyperconics. Mathematics 2020, 8, 429.

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