Regularities and Green's relations for finite sandwich semigroup T(X,Y;θ)
Lin Ping-feng · 2007
Let X and Y be nonempty sets,T(X,Y) be the set of mappings from X into Y,θ be an arbitrary but fixed mapping from Y into X for any α,β∈T(X,Y),the operation in T(X,Y) is defined by αβ=αθβ,where αθβ is the production of mappings.Then T(X,Y) forms a semigroup,called sandwich semigroup and denoted by T(X,Y;θ).The sandwich semigroup T(X,Y;θ) is called finite sandwich semigroup when both X and Y are finite sets and |X|,|Y|1.In this paper,we discuss the relationships of T(X,Y;θ),T(X;θ) and T_X,and study the regularity and Green's relations for(T(X,Y;θ).)