自由单演逆半群上的核—迹算子半群

Trace-Kernel Operator Semigroup of Free Monogenic Inverse Semigroup

对于逆半群上的同余ρ,在它的迹类中存在最大元ρT和最小元ρt.相应地,在它的核类中有最大元ρK和最小元ρk.因此,我们在S的同余格上得到四个算子Г={T,t,K,k}.本文将给出自由单演逆半群上,由算子半群Г生成的半群,即自由单演逆半群上的核一迹算子半群.

For congruence p on an inverse semigroup, there are maximal element pT and minimal element pt in a trace class; by the same token, there are maximal element pK and minimal element pk in a kernel class. So we can find four operators F = {K, k, T, t} on congruence lattice C（S） of an inverse semigroup S. In this paper, we gained extremum congruence which is not identity relation on free monogenic inverse semigroup Ix. Then establishing relations in F on congruence lattice C（S）, we obtain trace-kernel operator semigroup F＋/E＊ of Ix finally.