半群上的一类变换及其性质

A Translation of Semigroup and Its Properties

设S是一个半群,δ是S到S的一个映射,如果δ满足对于任意的x,y∈S,有δ(xyx)=xδ(y)x.则称δ为S的一个夹心变换.S的所有夹心变换的集合作成的半群称为S的夹心变换半群.本文讨论了夹心变换半群的一些性质,进一步利用夹心变换半群对一些特殊半群的进行了刻画.

Let S be a semigroup.A middle translation of S is a mapping 8 of S into S,such that S（xyx） = xδ（y）x for x,y∈S.The set of all middle translation of S forms a semigroup by usual product of mapping which is called a middle translation semigroup of S.In this paper,some properties of middle translation semigroup of S are given,fortherly some special semigroup is characterized by means of middle translation.