On Hyper P-Semi Simple I-algebra

In this paper we introduce the concepts of hyper P -semisimple Ialgebra and Abelian hyper I-algebra and we state and prove some related results. The hyper p-semi simple I-algebras is a generalization of p-semisimple BCI-algebras and a subclass of hyper I-algebras. Specially we show that every Abelian hyper I-algebra is a hyper psemisimple I-algebra and a commutative canonical hypergroup. In follow, we prove that every hyper p-semisimple I-algebra is a quasi hypergroup. Finally, we give some relationships among the notions of hyper p-semisimple I-algebras, Hv-groups, semigroups and hypergroups.