Regularity and Green's Relations on a Special Transformation Semigroup
Lei Sun, Cheng Zheag-xing · Journal of Mathematical Research and Exposition · 2007
Let T_X be the full transformation semigroup on a set X,and E an equivalence on X.Let T_E(X)={f∈T_X:■(x,y)∈E,(f(x),f(y)∈E}. Then T_E(X)forms a subsemigroup of T_X.If X is a totally ordered set and E is a convex equivalence on X,then let OP_E(X)be a semigroup consisting of all the orientation-preserving maps in T_E(X).In this paper,for the special convex equivalence E on a finite totally ordered set X,we describe the regular elements and characterize Green's relations on the semigroup OP_E(X).