有限弱Y-稳定变换半群的极小同余

摘要

Let T(X) be the full transformation semigroup on the finite set X, and Y a nonempty subset of X. Let W(Y) = {α∈T(X) : Yαα∪Y}. Prove that W(Y) exactly has two minimal congruences when 1< | Y| < | X| ; when |y| = |X| or1=|Y|<|X|,W(Y) has only one minimal congruence.%设T(X)为有限集X上的全变换半群,Y为X的任意非空子集,引入有限弱Y-稳定变换半群W(Y)={α∈T(x):Yα(∈)Y},证明了当W(Y)满足1＜|Y|＜|X|时,W(Y)有且仅有2个极小同余.另外,当| Y |=|x|(即Y=X)或1=|Y|＜|X|时,W(Y)只有唯一的极小同余.