偏序半群的偏序扩张

On extensions of partial orders of partially ordered semigroups

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.