有限部分变换半群的几类平凡子半群

Some Kinds of Trivial Subsemigroups of Finite Partial Transformation Semigroup

设X是集合,PX为X上的所有部分变换做成的半群。当X是有限集时,PX为周期半群。利用周期半群S是R-平凡的、L-平凡的和J-平凡的性质,给出了当X是有限集时,PX的子半群S是这几类平凡子半群的充要条件。

Let X be a set and PX the partial transformation semigroup on X.When X is a finite set, semigroup PX is periodic.Under the nature of periodic semigroup S is R-trivial, L-trivial and J-trivial as necessary and sufficient conditions of the semigroup S of PX are these kinds trivial semigroups.