Complete Parts and Subhypergroups in Reversible Regular Hypergroups

In this paper we analyse the center and centralizer of an element in the context of reversible regular hypergroups, in order to obtain the class equation in regular reversible hypergroups, by using complete parts. After an introduction in which basic notions and results of hypergroup theory are presented, particularly complete parts, then we give several properties, characterisations and also examples for the center and centralizer of an element for two classes of hypergroups. The next paragraph is dedicated to hypergroups associated with binary relations. We establish a connection between several types of equivalence relations, introduced by J. Jantosciak, such as the operational relation, the inseparability and the essential indistin-guishability and the conjugacy relation for complete hypergroups. Finally, we analyse Rosenberg hypergroup associated with a conjugacy relation.