On Intra-regular Ordered Gamma-semigroups

Authors

  • Niovi Kehayopulu Professor Docent Dr. University of Athens

Keywords:

po-Gamma-semigroup, intra-regular, ideal, prime ideal, semilattice (chains) of simple semigroups

Abstract

We study the decomposition of an intra-regular $po$-$\Gamma$-semigroup into simple components. Then we prove that a $po$-$\Gamma$-semigroup $M$ is intra-regular and the ideals of $M$ form a chain if and only if $M$ is a chain of simple semigroups. Moreover, a $po$-$\Gamma$-semigroup $M$ is intra-regular and the ideals of $M$ form a chain if and only if the ideals of $M$ are prime. Finally, for an intra-regular $po$-$\Gamma$-semigroup $M$, the set $\{(x)_{\cal N} \mid x\in M\}$ coincides with the set of all maximal simple subsemigroups of $M$. A decomposition of left regular and left duo $po$-$\Gamma$-semigroup into left simple components has been also given.

Author Biography

  • Niovi Kehayopulu, Professor Docent Dr. University of Athens

    Professor Docent Dr.

    University of Athens, Department of Mathematics,

    15784 Panepistimiopolis

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Published

2017-07-11

Issue

Section

Algebraic Geometry

How to Cite

On Intra-regular Ordered Gamma-semigroups. (2017). European Journal of Pure and Applied Mathematics, 10(4), 620-630. https://www.ejpam.com/index.php/ejpam/article/view/3010