保持两个等价关系的夹心半群的格林关系和正则性

Sandwich Semigroups of Transformations Preserving two Equivalence Relations

摘要: 设X,Y为非空集合,E,F分别为X,Y上的等价关系.称映射f:X→Y是EF-保持的,如果对任意x,y∈X,(x,y)∈E蕴涵(f(x),f(y))∈F.设T(XE,YF:θ)表示所有EF-保持的映射的集合,:θY→X是一个FE-保持的映射,对任意f,g∈T(XE,YF;θ),定义f g=fθg,则T(XE,YF;θ)在运算"。"下构成一个半群,称为保持等价关系EF的夹心半群,θ称为夹心映射.本文讨论了保持等价关系EF的夹心半群T(XE,YF;θ)上的格林关系以及正则元的特征.

Abstract: 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(...