结合环的一个定理

A theorem on associative ring

设R是半质环,a∈R.如果对任意的x∈R有正整数n=n(a,x),使得下面条件之一成立 1) (ax)~n-xa∈Z(R) 2) (ax)~n+xa∈Z(R) 那么 a∈Z(R).

Let R be a semiprime ring, a R.If for any x R, there exits positive integer n=n(a,x) satisfied one of the following conditions:1) (ax)n-xa Z(R)2) (ax)n+xa Zthen a Z(R)