环的交换性定理

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.

A Theorem on the Commutativity of Rings

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=0α_iy~ixy~(K-i)+f_1(x,y),f_1(x,y) is a polynomial with integral coefficients,and every of x 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)∑k]i=0α_i=1,let f(a,b),c]=0.The corollary of this paper: If the K the half-simplicial rings satisfies condition(A),then the rings can be commutative.This is the integrate corollary of some conclusions.