On a-Maximal Ideals and C-Ideals of Ordered $\Gamma$-Semigroups

Jian Tang, Xiang-Yun Xie

Abstract

In this paper, we first introduce the  concept of $a$-maximal ideals in ordered $\Gamma $-semigroups and give some characterizations of $a$-maximal ideals of ordered $\Gamma $-semigroups. Furthermore, the concept of $C$-ideals in ordered $\Gamma $-semigroups is introduced. Some results on semigroups containing no maximal ideals are extended to ordered $\Gamma $-semigroups.