摘要
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。
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 ν 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 fmite sets and ｜ X ｜, ｜ Y｜ 〉 1. In this paper, we discuss the relationships of T（X,Y;θ）, T（X;θ） and Tx, and study the regularity and Green＇s relations for T（X,Y;θ）.
出处
《贵州师范大学学报（自然科学版）》
CAS
2007年第1期81-84,共4页
Journal of Guizhou Normal University：Natural Sciences
