On Characteristics of Hyperfields Obtained as Quotients of Finite Fields

2018/10/07 by A. Frigo, Frigo, Antonio, Hahn Lheem +3 · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1810.04035

openalex publication_date 2018/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hyperstructures are a natural extension of regular algebraic structures in which one of the operations, known as the hyperoperation, is multivalued; a hyperfield is such an extension on a field. M. Krasner (1962) proved that the quotient \mathbbF_p/G, where G is a subgroup of units in \mathbbF_p is a hyperfield. The characteristic of a field may be explicitly determined from the order of the field, but there are no existing generalizations for determining the characteristic of a hyperfield of the form \mathbbF_p/G. We show that for odd primes p, there exists an explicit form for the characteristic of the hyperfield \mathbbF_p/G and |G|=1,2,3,4. Finally, we prove a general form of the characteristic for hyperfields where |G| is prime.

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