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

Downloads

Published

2017-07-11

How to Cite

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

Issue

Section

Algebraic Geometry

Most read articles by the same author(s)

1 2 > >>