有限夹心半群T(X,Y;θ)的正则性与Green关系

设X,Y是非空集合。记T(X,Y)为X到Y的映射全体构成的集合,θ是Y到X的一个确定的映射,α,β∈T(X,Y),定义运算:αβ=αθβ,这里,αθβ表示一般映射的合成。则T(X,Y)关于运算构成一个半群,称为夹心半群T(X,Y;θ)。当X,Y都为有限集合且|X|>1,|Y|>1时,称夹心半群T(X,Y;θ)为有限夹心半群。讨论了T(X,Y;θ)、T(X;θ)和TX之间的联系,研究了有限夹心半群T(X,Y;θ)的正则性和G reen关系。

Regularities and Green''''s relations for finite sandwich semigroup T(X,Y;θ)

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 αβ=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).)