Principal filters of some ordered Γ -semigroups

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Submitted: 2024-12-18; Published: 2024-12-18

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Abstract

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