Niovi Kehayopulu - Department of Mathematics, University of Athens, P.O.Box ۱۶۷۸۴, Athens, Greece

An important problem in the theory of ordered hypersemigroups is to describe the ordered hypersemigroups which enter their properties into their σ-classes. In this respect, we prove the following: If H is a regular, left (right) regular, completely regular, intra-regular, left (right) quasi-regular, semisimple, k regular, archimedean, weakly commutative, left (right) simple, simple, left (right) strongly simple ordered semigroup and σ a complete semilattice congruence on H then, for each a ∈ H, the σ-class (a)σ of H is, respectively, so.

Ordered hypersemigroup, regular, left regular, intra-regular, left quasi-regular, semisimple, k-regular, archimedean, weakly commutative, left simple, simple, left strongly simple, complete semilattice congruence