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Article

 -hypergroups and  -semihypergroups associated to binary relations

b. davvaz

Abstract

the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary relations and give necessary and sufficient conditions on a set of binary relations  on a non-empty set s such that s becomes a  -semihypergroup or a  -hypergroup

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