A Brief Survey on the two Different Approaches of Fundamental Equivalence Relations on Hyperstructures

Abstract

Fundamental structures are the main tools in the study of hyperstructures. Fundamental equivalence relations link hyperstructure theory to the theory of corresponding classical structures. They also introduce new hyperstructure classes.The present paper is a brief reference to the two different approaches to the notion of the fundamental relation in hyperstructures. The first one belongs to Koskas, who introduced the β ∗ - relation in hyperstructures and the second approach to Vougiouklis, who gave the name fundamental to the resulting quotient sets. The two approaches, the necessary definitions and the theorems for the introduction of the fundamental equivalence relation in hyperstructures, are presented.