摘要本文讨论了一类满足多项恒等式的环的交换性,推广了文[1]的结果,证明了: (1) R为一个结合环,且对任意x,y∈R, a1xy2+a2xyx+a3x2y+a4yx2+a5y2x+a6yxy∈Z(R) 这里a1(i=1,2…6)是整数且sum from i=1 to 6(a1=0),如果下文中条件(Ⅰ,Ⅱ和Ⅲ)之一满足,那么R为交换环。(2)
Abstract:The main results are the following theorems; Theoeeml Let R be an associative ring, for x, y∈R,a1xy2+a2xyx+a3x2y+a4yx2+a6y2x+a6yxy∈Z(R),where ai(i=1, 2, 3, 4, 5, 6) are integers With sum from i=1 to 6 (a1)=0.R is commutative, if anyone of anyone o