On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups

Abstract EN

We introduce the notion of ordered quasi-Γ-ideals of regular ordered Γ-semigroups and study the basic properties of ordered quasi-Γ-ideals of ordered Γ-semigroups.

We also characterize regular ordered Γ-semigroups in terms of their ordered quasi-Γ-ideals, ordered right Γ-ideals, and left Γ-ideals.

Finally, we have shown that (i) a partially ordered Γ-semigroup S is regular if and only if for every ordered bi-Γ-ideal B, every ordered Γ-ideal I, and every ordered quasi-Γ-ideal Q, we have B∩I∩Q⊆BΓIΓQ and (ii) a partially ordered Γ-semigroup S is regular if and only if for every ordered quasi-Γ-ideal Q, every ordered left Γ-ideal L, and every ordered right-Γ-ideal R, we have that R∩Q∩L⊆RΓQΓL.