Dariush Heidari - Faculty of science, Mahallat Institute of Higher Education, Mahallat, Iran

Breakable semihypergroups, defined by a simple property: every non-empty subset of them is a subsemihypergroup. In this paper, we introduce a class of semihypergroups, in which every hyperproduct of n elements is equal to a subset of the factors, called \pi_n-semihypergroups. Then, we prove that every semihypergroup of type \pi_{۲k}, (k\geq ۲) is breakable and every semihypergroup of type \pi_{۲k+۱} is of type \pi_۳. Furthermore, we obtain a decomposition of a semihypergroup of type \pi_n into the cyclic group of order ۲ and a breakable semihypergroup. Finally, we give a characterization of semi-symmetric semihypergroups of type \pi_n.

Breakable semihypergroup, Hypergroup, Hyperproduct, Semihypergroup of type \pi_n