高阶差分的表达式与环的交换条件  

Expressions of Difference of Higher Order and a Condition for Commutativity of Rings

作　　者：傅昶林 韩见知 

出　　处：《哈尔滨科学技术大学学报》1989年第3期123-128,共6页

摘　　要：本文给出了非结合环上高阶差分的精确表达式,井由此证明了:设 R 为有1之非结合环,则当具有下列两条件时:(1)R 中任何元素 x,y 满足 F(x,y)=0,(2)R 是 P-扭自由的。R 是交换的。此处 P 是诸 P_i 的最大正公因数,而 P_i=(m_i-1)!(n_i-1)!q_i 适于1≤i≤d或 i=α,i=β。in this paper exact expressions of difference of higher order on non-asso- ciative rings are given and the following theorem is proved. Theorem.Let R be a non-associative ring with 1.If R satisfies the follo- wing two conditons: (1)F(X,Y)=0 for all X,Y∈R. (2)R is a p-torsion free,where P is a positive maximal common factor in all p_i for p_i=(mi-i)!(n_i-1)!q_(?)and 1≤i≤d or i=α and i=β. Then R is commutative. Moreover the cases in Which R is an associative ring and semi-prime ring are respectively discussed.

关 键 词：非结合环 高阶差分 算子 多项式 

分 类 号：O153.3[理学—数学]