Sandwich Semigroups of Transformations Preserving two Equivalence Relations
WU Yong-fu · Journal of Xinyang Normal University · 2008
Let X,Y be nonempty set and E,F be equivalences on X and Y,respectively.Let θ:Y→X be a fixed function.Let T(XE,YF;θ)be the collection of all functions from X and into Y such that(x,y)∈E implies(f(x),f(y))∈F.We define an operation。on T(XE,YF;θ) by f。g=fθg for any f,g∈T(XE,YF;θ).Then T(XE,YF;θ) forms a seminroup under the operation which is called sandwich semigroup with the sandwich function θ.In this paper,we characterize Green's equivalences and describe the regular elements of the semigroup T(XE,YF;θ).