STUDY ON THE STRUCTURE OF Γ-SEMIHYPERGROUPS

In this article, we study Gamma-semihypergroups introduced recently. We introduce the hyper versions of Green's relations in Gamma-semihypergroups and give some related characterizations. We introduce the n-prime Gamma-hyperideal and n-semiprime Gamma-hyperideal of a Gamma-semihypergroup and show that for any integer n >= 2, n-prime Gamma-hyperideals are a generalization of prime Gamma-ideals. We also give the relationship between n-prime Gamma-hyperideals and Gamma-hyperideal extensions in Gamma-semihypergroups. Then, we deal with prime ideal and introduce the notion of prime radical in a Gamma-semihypergroup M, and also, we obtain some results and relations among the prime radicals of M and S, where S is the left operator semihypergroup of M.