半质环的交换性条件

本文改进了1]中定理1,定理2及文2]中的一个结果,并给出半质环另外一个交换性条件.

On the Commutative Conditions for Semiprime Rings

In this paper1], Guo xiuzhan gave two commutative results for semiprime rings. In this paper, we generalize his results. In paper2], H·A·S·Abujabal and M. S. khan proved that suppose R be a semiprime ring and there exists a positive integer n such that xn, y]-x,yn]∈ Z(R) and xn+1,y]-x,yn+1] ∈ Z(R) for all x,y in R, then R is commutative. We prove that if a semiprime ring R satisfy the followingcondition: There exist positive integers m,n with m > 1 and n > 1 such that xm,y] -x,yn] ∈ Z(R) for all x,y in R, then R is commutative, we also give an other commutative result for semiprime ring.