On Intra-regular Ordered Gamma-semigroups
Keywords:
po-Gamma-semigroup, intra-regular, ideal, prime ideal, semilattice (chains) of simple semigroupsAbstract
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.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
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.