有限部分变换半群的幂等元生成集

Idempotent generators in finite partial transformation semigroup

设Xn={1,2,...,n},Pn是Xn上的所有部分变换所构成的半群,Sn是Xn上的n次对称群,SPn=Pn\Sn,I是SPn中具有类(n,n-1)和(n-1,n-1)的幂等元所构成的集合。

Let Xn = {1,2,... n} , Pn is semigroup consisting of all partial transformations in Xn,the symmetric group of all permutations of Xn is denoted by Sn, SPn = Pn／Sn ,I is a set of idempotents of having （ n, n - 1 ） - classes and （ n - 1, n - 1 ） - classes, we shall show that 〈I〉 = SPn if and only if the associated digraph D（I） is strong, complete and self- loop.