K-半单纯环的一个交换性定理

摘要

为了促进交换性的发展,根据半质环及半单环的相关资料,推广了戴跃进的结论,提出并严格地证明了一个kothe半单纯环的交换性定理:若R是一个kothe半单纯环,且对(V)a.b,c∈R,都存在一个正整数k=k(a,b),一含有x2和n=n (a,b,c)(≥k)个y的字fx(x,y)及一整系数多项式φx(x,y)使得[Σki=0αibiabk-i-fx(a,b)φx(a,b),c]∈Z(R) (1)其中|Σki=0αi|=1,则R是交换环.%For the rapid development of commutative, a commutative theorem of rings were given in this paper, Dai Yuejin' conclusion was expended and one commutative theorem on kothe e-semisimple rings is put forward and proved strictly:If R was a kothe -semisimple rings,and for arbitrary a,b,c ∈ R, there existed a positive integer k = k(a,b) ,a word fx(x,y) containing x and n =n(a,b,c) (≥k) y's, and a polynomial φx(x,y) with integer coefficients such that [∑ki=0αiβiabk-I-fx(a,b)φx(a,b) ,c] ∈Z(R) (1)|∑ki=0αi|=1 then R was commutative.