a Faculty of Mathematics, “Al.I. Cuza” University, Bd. Carol I, no. 11, 700506 Ia?i, Romania b Faculty of Mathematics and Informatics, “Ovidius” University, Bd. Mamaia 124, 900527 Constan?a, Romania
Abstract:
Different partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations ρ and σ on H we investigate when the hypergroups associated with the relations ρ∩σ, ρ∪σ and ρσ are reduced. We also determine when the cartesian product of two hypergroupoids associated with a binary relation is a reduced hypergroup.