On Hybrid Pure Hyperideals in Ordered Hypersemigroups

Abstract

In this paper, the concepts of hybrid pure hyperideals in ordered hypersemigroups are introduced and some algebraic properties of hybrid pure hyperideals are studied. We characterize weakly regular ordered hypersemigroups in terms of hybrid pure hyperideals. Finally, we introduce the concepts of hybrid weakly pure hyperideals and prove that the hybrid hyperideals are hybrid weakly pure hyperideals if such hybrid hyperideals satisfy the idempotent property.