关于内正则Duo序半群  

On intra-regular and duo ordered semigroups

作　　者：施智杰[1,2] 

机构地区：[1]西北大学数学系,陕西西安710127 [2]山西大同大学数学与计算机科学学院,山西大同037009

出　　处：《纺织高校基础科学学报》2008年第4期393-397,共5页Basic Sciences Journal of Textile Universities

摘　　要：给出内正则duo序半群的刻划,证明一个序半群S是内正则duo的当且仅当它是单且左单且右单的半群半格.特别地,S是单且左单且右单的序半群链当且仅当S是内正则duo的且S的所有理想关于集合的包含关系构成链.The characterizations of intra-regular and duo ordered semigroups are given, and the result that an ordered semigroup is intra-regular and duo ordered semigroups are given,and the result that an ordered semigroup is intra-regular and duo if and only if it is a semilattice of intra-regular and simple and left simple and right simple sub-semigroups is proved. Particularly, S is a chain of simple and left simple and right simple ordered semigroups if and only if it is intra-regular and duo and the ideals of S form a chain with respect of inclusion.

关 键 词：内正则序半群 duo序半群 理想 单(左单 右单)序半群 

分 类 号：O152.7[理学—数学]