Strongly regular relations on regular hypergroups

Hypergroups that have at least one identity element and where each element has at least one inverse are called regular hypergroup. In this regards, for a regular hypergroup H, it is shown that there exists a correspondence between the set of all strongly regular relations on H and the set of all normal subhypergroups of H containing S_{beta}. More precisely, it has been proven that for every strongly regular relation $\rho$ on H, there exists a unique normal subhypergroup of H containing S_{beta}, such that its quotient is a group, isomorphic to H/rho. Furthermore, this correspondence is extended to a lattice isomorphism between them.