T_E(X)的由幂等元生成的子半群

A subsemigroup generated by the idempotents of T_E(X) ZOU Ding-yu,PEI Hui-sheng,WANG Shi-fei

设X为有限集合,TX为X上的全变换半群,设E为X上任一非平凡等价关系,变换半群TE(X)定义为TE(X)={f∈TX∶ (a,b)∈E,(f(a),f(b))∈E}.讨论了半群TE(X)的由幂等元生成的子半群T2,以及由亏值为1的幂等元作为生成元时,T2的极小生成元集,并且求出了这个极小生成集的元素个数.

Let X be a finite set, T_X be the full transformation semigroup on X,E an equivalence on X. The transformation semigroup T_E(X) is defined asT_E(X)={f∈T_X∶(a,b)∈E,(f(a),f(b))∈E}.A subsemigroup of T_E(X),which is generated by the idempotents of T_E(X),is considered.It is shown that a mininal generating set ∪~r_(i=1)M~*_i of the idempotents with defect 1 must contain 12(∑~r_(i=1)(｜A_i｜)(｜A_i｜-1)) members.