Hypergroups and hyperfields in universal algebra

TL;DR

This paper develops a framework for transferring results from semigroup theory to hyperstructures like hypergroups and hyperfields using power semigroups with negation, enriching universal algebra.

Contribution

It introduces a method to lift hyperstructures to power semigroups with negation, enabling the transfer of universal algebra results to these structures.

Findings

Established a transfer method from semigroup theory to hyperstructures.

Applied the method to hypergroups, hyperfields, and hypermodules.

Connected the theory to examples from Baker's work.

Abstract

Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer the general theory from universal algebra. Special attention is given to the examples from Baker's article.