关于Petrich和Reilly的一个问题

摘要

本文研究了M.Petrich和N.R.Reilly的一个公开问题:即整体关系的下运算是否为一个完全同态.利用Clifford半群上的同余刻画,得到了该运算不是一个∩-同态.从而解决了上述公开问题.%In this paper, we consider an open problem of M. Petrich and N. R. Reilly: Is the operator of lower global relation a complete homomorphism? By using congruences on a Clifford semigroup, we get that, in general, the operator is not a ∩-homomorphism. Therefore the problem is solved.