On intra-regular and left regular and left duo ordered Γ-semigroups

الأصل · EN

For an intra-regular or a left regular and left duo ordered Γ-semigroup M, we describe the principal filter of M which plays an essential role in the structure of this type of po-Γ-semigroups. We also prove that an ordered Γ-semigroup M is intra-regular if and only if the ideals of M are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of M are semiprime.