半群T_n(k)的正则性和Green关系

Regularity and Green's relation on the semigroup T_n(k)

设T_n是[n]={1,…,n}上的全变换半群.对任意1≤k≤n,令Tn(k)={α∈T_n|x∈[n],x≤kxα≤k},则Tn(k)是Tn的子半群.刻画了半群GT_n(k)的正则元的特征,并描述了该半群上的Green关系.

Let T, be the semigroup of all full transformations of [n]={1,…,n}. For 1≤k≤n ,let Tn（k）={α∈T_n｜x∈[n],x≤kxα≤k}. Then Tn（k） is a suhsemigroup of Tn. The characterization of regular elements and Green＇s relations are given on the semigroup Tn（k）.