Kthe半单环,Bear半单环的交换性条件

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|_x=1,|w|_y≥|c|_y,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.

On the Commutativity Conditions for kothe Semi-simple Rings and Bear Semi-simple Rings

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 paper10], 9] repectively.