偏序半群的拟序和商拟序的一种构造方法

A Constructive Method on Pseudo order and Quotient Pseudo order of Partially Ordered Semi-groups

设ρ是偏序半群S的拟序(或商拟序).主要从偏序商半群Sρ(ρ=ρ?ρ-1)的拟序和商拟序出发,来研究S的拟序和商拟序.首先,通过Sρ的拟序和商拟序,给出了S的拟序和商拟序的一种构造方法.其次,分别讨论了Sρ的包含拟序μ的拟序集和S的拟序集以及Sρ的包含商拟序μ的商拟序集和S的商拟序集之间的关系,特别地,证明了Sρ的包含拟序μ的拟序集和商拟序集与S的特殊拟序集和商拟序集之间存在保持包含关系的双射的重要结论.

Let ρ is pseudo order(or quotient pseudo order) of partially ordered semi-groups S, The main aim of this paper is to study pseudo order and quotient pseudo order of S from pseudo order and quotient pseudo order ofpartially ordered quotient semigroups S ρ( ρ= ρ ? ρ-1). Firstly, by pseudo order and quotient pseudo order of S ρ, a constructive method on Pseudo order and quotient pseudo order of S are given. Secondly, relations between pseudo order set and quotient pseudo order set including pseudo order μ of S ρ and pseudo order set and quotient pseudo order set of S are separately discussed, especially, it is proved that there exists inclusion relation-preservingbijective of pseudo order set and quotient pseudo order set including pseudo order μ of S ρ and special pseudo order set and quotient pseudo order set of S.