一类保序压缩变换半群的Green关系

The Green's Relations upon Order-Preserving Transformation Semigroup

设Xn={1,2,…,n},Q(Xn)={A1,A2,…,Ar}为Xn上任意一个划分,令OCT(Xn)={α∈On:Ai,Aj∈Xn,d(Aiα,Ajα)≤d(Ai,Aj)},则OCT(Xn)是一个半群。本文刻划了该半群的Green关系及一些相关的性质。

Let ＂X n＂be finite set with ＂n＂ elements,and Q（Xn）={A1,A2,…,Ar}be an arbitrary partition of ＂Xn＂.And let OCT（Xn）={α∈On：Ai,Aj∈Xn,d（Ai,α,Ajα）≤d（Ai,Aj）},then OCT（Xn）is a semigroup.This paper describes the Green＇ s Relations of OCT（X n）and some related properties.