Principal filters of some ordered $\Gamma$-semigroups

Authors

  • Niovi Kehayopulu Department of Mathematics University of Athens 15784 Panepistimiopolis, Athens, Greece
  • Michael Tsingelis Hellenic Open University School of Science and Technology Studies in Natural Sciences, Greece

Abstract

For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-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.

 

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Published

2016-12-22

How to Cite

Kehayopulu, N., & Tsingelis, M. (2016). Principal filters of some ordered $\Gamma$-semigroups. Armenian Journal of Mathematics, 8(2), 96-103. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/127

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Articles