Table of Contents
Algebra
Volume 2013, Article ID 565848, 7 pages
http://dx.doi.org/10.1155/2013/565848
Research Article

On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups

Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India

Received 31 March 2013; Accepted 7 October 2013

Academic Editor: Sorin Dascalescu

Copyright © 2013 M. Y. Abbasi and Abul Basar. 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.

Abstract

We introduce the notion of ordered quasi- -ideals of regular ordered -semigroups and study the basic properties of ordered quasi- -ideals of ordered -semigroups. We also characterize regular ordered -semigroups in terms of their ordered quasi- -ideals, ordered right -ideals, and left -ideals. Finally, we have shown that (i) a partially ordered -semigroup is regular if and only if for every ordered bi- -ideal , every ordered -ideal , and every ordered quasi- -ideal , we have and (ii) a partially ordered -semigroup is regular if and only if for every ordered quasi- -ideal , every ordered left -ideal , and every ordered right- -ideal , we have that .