偏序半群的偏序扩张  

On extensions of partial orders of partially ordered semigroups

作　　者：邵海琴[1,2] 薛占军[2] 雷振亚[3] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741000 [2]西北大学数学系,陕西西安710127 [3]西安电子科技大学电子工程学院,陕西西安710071

出　　处：《纯粹数学与应用数学》2008年第4期730-735,共6页Pure and Applied Mathematics

基　　金：陕西省自然科学基金(2005A15)

摘　　要：引入了偏序半群(S,·,≤)上的半拟序σ及模σ半拟链的概念.通过模σ半拟链,将S的偏序≤扩张为≤*,讨论了(S,·,≤*)是偏序半群的充分条件,并获得了若干理想的结果.特别地,得到了SPO(S)到PO(S)的两个半格同态定理.最后,还给出了S的满足某些给定条件的有限子集在≤*下成链的充要条件.In this paper, firstly, the concepts of semi-pseudoorder and semi-pseudochain mod σ on the partially ordered semigroup （S,·, 〈） is introduced. Secondly, a sufficient conditions for extending a partial order of S to another partial order by semi-pseudochain is given, and obtain some interesting results. In particular, two semilattice homomorphism theorem are obtained. Finally, sufficient and necessary conditions for extending a partial order of S to another partial order such that some finite subsets satisfying some conditions of S form a chain.

关 键 词：偏序半群 偏序扩张 半拟序 半拟链 有限全序扩张 

分 类 号：O152.7[理学—数学]