环的交换性定理

A Theorem on the Commutativity of Rings

设条件(A)为:若对任意的a,b,c∈R,存在依赖于a,b,c的整系数多项式f(x,y),f(x,y)形如∑ki=0αiyixyK-i+f1(x,y),f1(x,y)为一整系数多项式,其每一项关于x的次数2,关于y的次数K(此处K=K(a,b)为依赖于a,b的正整数),∑i=0αi=1,使[f(a,b),c]=0.结论为:满足条件(A)的K the半单纯环是交换的.这是一些结论的统一推广.

Let condition （A）.. if for any a, b, c ∈ R, there is a polynomial with integral coefficients f（x, y） which depended on a ,b,c. f（x,y） such that ∑^k i=0 αiy^ixy^k-i＋f1（x,y）,f1（x,y）is a polynomial with integral coefficients, and every ofx is not smaller than 2, the degree of y is not smaller than k（k = k（a,b） and k is positive integral which depended on a,b）. The corollary of this paper： If the Koethe half-simplicial rings satisfies condition （A）, then the rings can be commutative. This is the integrate corollary of some conclusions.