半素环的一个交换性定理

A COMMUTATIVITY THEOREM FOR SEMIPRIME RINGS

本文证明了:在半素环R中,如果存在正整数m,n且n>1,使得对任意x,y∈R有(xy^m)~n-x^my∈Z(R)(R的中心),那么R是交换环。

In this paper, the following theorem is proved: Let R be a semiprime ringsatisfying (xy^m)~n-x^ny∈Z(R) for all x, y∈R where m, n are fixed positiveintegers, n>1, then R is commutative.