(untitled) (European Journal of Pure and Applied Mathematics, 2018)
We give some information concerning the Green’s relations R and L in hypergroupoids extending the concepts of right (left) consistent or intra-consistent groupoids in case of hypergroupoids. We prove, for example, that if an hypergroupoid H is right (left) consistent or intra-consistent, then the Green’s relations R and L are equivalence relations on H and give some conditions under which in consistent commutative hypergroupoids the relation R (= L) is a semilattice congruence. A commutative hypergroupoid is right consistent if and only if it is left consistent and if an hypergroupoid is commutative and right (left) consistent, then it is intra-consistent. A characterization of right (left) consistent (or intra-consistent) right (left) simple hypergroupoids has been also given. Illustrative examples are given.