t 次正规环的一个恒等式定理及其应用  

AN IDENTITY THEOREM IN NORMAL RINGS OF DEGREE t AND ITS APPLICATION

作　　者：郑玉美[1] 

机构地区：[1]湖北大学

出　　处：《数学杂志》1993年第1期53-58,共6页Journal of Mathematics

摘　　要：一个适合 t 正规多项式的环叫做 t 次正规环。本文得到一个关于 t 次正规环的恒等式定理,并在此定理基础上得出交换环的另一些恒等式,它们是著名的环的交换性问题的一些结果或类似的结果。If a ring R Satisfies a t normal identity f(x_1,…,x_d),we say R is anormal ring of degree t.In this paper we obtain the follewing theoremTheorem Suppose a polynomial F(x_1,…,x_t,x_(t+1))∈Z{x},deg_1F=n_1 is thedegree of F at X_1,F_1 is the sum of all monomials h with deg_1h=n_1,alsodeg_2F_1=n_2 is the degree of F_1 at X_2,F_2 is the sum of all monomials h withdeg_2h=n_2,etc.If t is an even number,and (?)x_i∈R,1≤i≤t,a_i∈{x_i,x_i+1,…,x_i+n_i}F(a_1,…,a_i,[a_1,…,a_t])=0Then n_1!…n_i!IF_i(1,…,1,[x_i,…,x_i,])=0.Where[x_1,…,x_t]=S_i(x_1,…,x_i,)=∑(Sgπ)X_(π1),…X_(πi)(?)As application we also give some commutativity conditions of rings.

关 键 词：正规环 恒等式定理 交换环 

分 类 号：O153.3[理学—数学]