Green's Relations on P_E(X,R)
Jia Geng-hua · Journal of Xinyang Normal University · 2009
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.