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A Class of Regular Congruences on Ordered Semigroups

In this paper,the notation of a strongly ordered congruence on an ordered semigroup S is introduced.Some properties of strongly ordered congruences are given.The results that the strongly ordered congruences are the strongly regular congruences and that the converses are not true are proved.In the Section 3,we also prove that the set SOC(S) of all strongly ordered congruences on an ordered semigroup S is a V-complete distributive sublattice of the lattice C(S) of all congruences on S with respect to the intersection defined as usual and the union (also called transitive product).