P_E(X,R)的Green关系

Green s Relations on P_E(X,R)

摘要: 设X为非空集合,PX为X上的部分变换半群,设E为X上的一个等价关系,R为商集X/E的横断面(即在每个等价类中取一个元素所组成的集合).对于每个x∈domf,记rx为R中的元素,满足(x,rx)∈E.定义PE(X,R)=f∈PX∶x,y∈domf,(x,y)∈E■(f(x),f(y))∈E,x∈dom f■rx ∈domf,f(rx)∈R.则PE(X,R)作成PX的子半群.本文主要讨论PE(X,R)的Green关系.

Abstract: Let X be a nonempety set,PX the semigroup of all partial transformations on the set X.Let E be an equivalence relation on X and R the cross-section of the quotient set X/E.For x∈dom f,denote by rx the element of R with(x,rx)∈E.Define PE(X,R)=f∈Px∶x,y∈dom f,(x,y)∈E■(f(x),f(y))∈E,x∈dom f■rx∈dom f,f(rx)∈R.Then PE(X,R)formes a subsemigroup of PX.In this paper,Green s equivalences of PE(X,R) are discussed.