LAUSR

The concept of Γ -hypersemigroup has been introduced in Turk J Math 2020; 44 (5): 1835-1851 in which it has in which it has been shown that various results on Γ -hypersemigroups can be obtained directly as corollaries of more general results from the theory of le -semigroups (i.e. lattice ordered semigroups having a greatest element) or poe -semigroups. As a continuation of the paper mentioned above, in the present paper, the concept of ordered Γ hypersemigroups has been introduced, and their relation to lattice ordered semigroups is given. It has been shown that although the results on ordered Γ -hypersemigroups cannot be obtained as corollaries to the corresponding results of le or poe -semigroups, still the main idea comes from the le -semigroups or poe -semigroups, and the proofs go along the lines of the le or poe -semigroups.