Inverse Semihypergroups

Abstract

The concept of inverse semihypergroup is a generalization of the concept of inverse semigroup. In this paper we defined an orthodox semihypergroup S as it is a regular semihypergroup in which the set of idempotents of S forms a subsemihypergroup. We also presented a new definition of inverse semihypergroup S as each element x ∈ S has a unique inverse s −1 in S, and we provided many results related to inverse semihypergroups, regular semihypergroups and orthodox semihypergroups