摘要
本文首先给出Kothe半单环的一个交换性定理：设R是Kother半单环，如果对任意的x,y∈R，存在依赖于x和y的两个字w(X,Y),c(X,Y)使w(x,y)-c(x,y)∈（C（R），其中│w│x>1,│c│=1,│w│y≥│c│，则R是交换环。该定理大大改进了文[7][8]结果，然后给出Bear半单环的几个交换性定理，改进了文[9][10]的几个结果。
In this paper, we give a commutative theorem for kothe semi -simple rings at first; Let R be a kothe semi -simple ring statisfying that for any x,y in R, there exist two words w and r with |w |x>1, |τ|x = 1,|w|y≤|T|y such that w(x,y) - τ(x,y) ∈c(R) . then R is commutative. After this, we prove some commutativity results for Bear semi -simple rings , which improve some results given by Guo xiu zhen and Guo Yuan chuen in paper[10], [9] repectively.
