摘要
本文引入了偏序半群中Ｃ左理想的概念，讨论了Ｃ左理想的一些基本性质，定义了左基的概念并利用它给出了最大Ｃ左理想存在的必要和充分条件．作为应用，本文还讨论了每个真左理想均为Ｃ左理想和无Ｃ左理想这两类半群的结构特征．
In this paper we introduce and study the C-left ideals of ordered semigroups. We discuss some elementary properties of C-left ideals, and give out the sufficient and necessary conditions of the existence of the greatest C-left ideal of an ordered semigroup by the concept of left bases of an ordered semigroup which is introduced in this paper. As an application, we characterize two classes ordered semigroups: C-left simple ordered semigroups and ordered semigroups which every proper left ideal is C-left ideal. The corresponding results on semigroups——without order——are obtained as an application of the results of this paper in the way indicated in .
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1997年第6期861-866,共6页
Acta Mathematica Sinica：Chinese Series
基金
广东省自然科学基金
国家教委博士点专项基金
关键词
C-左理想
最大C-左理想
偏序半群
半群
C-left ideal, Left base, Maximal L-class, Greatest C-left ideal
