h - Relation and Its Associated Hyperstructures
نویسندگان
چکیده
An h-relation on a non-empty set S is in fact a relation from S to the power set P (S) of S. Here, in this paper, it is shown that the semigroup of binary relations on a set S can be embedded as a subsemigroup into the semigroup of h-relations on S(with restpect to a suitably defined operation). We have introduced and studied here two types of reflexivities, symmetries and transitivities of h-relations. The conditions imposed on an h-relation R, under which the hyperstructure HR ( induced by the h-relation R on a non-empty set H) can necessarily and sufficiently be a semihypergroup or a hypergroup, have been obtained. We have established further the necessary and sufficient conditions for which a given semihypergroup (H, ◦) can be induced by a specified h-relation R. 2000 Mathematics Subject Classification: 20N20
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