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 duoordered Γ-semigroupM, we describe the principal filter ofMwhich plays an essential role in the structure of this type ofpo-Γ-semigroups. We also prove that an ordered Γ-semigroupMisintra-regular if and only if the ideals ofMare semiprime and itis left (right) regular and left (right) duo if and only if the left(right) ideals ofMare semiprime.