满足(xy)~k=x^ky^k半质环的交换性

The Commutative of Semi-prime Ring Satisfying Condition (xy)k =xkyk

证明了满足条件<α>的半质环R含有正则元时是交换环.<α>:(?)x,y∈R有依于它们的自然数n=n(x,y),使(xy)n+i=xn+iyn+i,i=0,1,2成立.

In this paper the following theorem will be proved: Let R be a semi-prime ring with normal element. If R satisfies the condition <α>,R is commutative. <α>:For (?)x, y∈R, there is an integer n= n(x, y), depending possibly on x, y, such that (xy)n+i=xn+iyn+i,i= 0, 1, 2.