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    Author(s)

    Niovi Kehayopulu
    Category: Mathematics
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      Natural Science, Biology, 2025

      Principal filters of some ordered Γ -semigroups

      Niovi Kehayopulu
      This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

      © 2025 by author(s) and The Gufo Inc.
      CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

      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.

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