Existence theorem of finite Krasner hyperfields

TL;DR

This paper proves that for every integer n ≥ 2, there exists a Krasner hyperfield of order n, establishing their universal existence across all such sizes.

Contribution

It provides a general existence theorem for Krasner hyperfields of any finite order n ≥ 2, filling a fundamental gap in hyperfield theory.

Findings

Existence of Krasner hyperfields for all n ≥ 2

Construction methods for finite Krasner hyperfields

Theoretical proof of hyperfield existence

Abstract

The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greater than or equal to 2.