On C-ideals and the basis of an ordered semigroup

AIMS Mathematics

Ze Gu¹  Xiang-Yun Xie²  Jian Tang³ 

[1] 1 School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P. R. China;2 School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong, P. R. China;3 School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P. R. China;

关键词: ordered semigroup;    greatest ideal;    c-ideal;    basis;    greatest c-ideal;   

DOI  :  10.3934/math.2020245

来源: DOAJ

【 摘 要 】

In this paper, we characterize ordered semigroups containing the greatest ideal and give the conditions of the greatest ideal being a C-ideal in an ordered semigroup. Moreover, we introduce the concept of a basis of an ordered semigroup and study the relationship between the greatest C-ideal and the basis in an ordered semigroup.