On ordered Γ-hypersemigroups, minimal bi-ideals, and minimal left ideals

Abstract

The definition of ordered Γ-hypersemigroups and the definitions of regular and intra-regular ordered Γhypersemigroups in the existing bibliography should be corrected. Care should be given to the definitions of bi-Γhyperideals and quasi-Γ-hyperideals as well. The main results are a characterization of minimal bi-ideals of an orderedΓ-hypersemigroup S in terms of B-simple bi-ideals of S and a characterization of minimal left (resp. right) ideals ofan ordered Γ-hypersemigroup S in terms of left (resp. right) simple subsemigroups of S