关于半质环交换性的注记  

A note on the commutativity of semiprime rings

作　　者：朱捷[1] 于宪君[1] 

机构地区：[1]哈尔滨商业大学基础科学系,黑龙江哈尔滨150076

出　　处：《黑龙江大学自然科学学报》2003年第3期34-35,共2页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省自然科学基金资助项目(A9818);黑龙江省教育厅科研项目(9543007)

摘　　要：设R为结合环。文献[3]证明了:设R是具有正则元的半质环,如果R满足条件:对于任意的x,y∈R,都存在一个与x,y有关的整数n=n(x,y)≥1,使得(xy)n+k=xn+kyn+k,k=0,1,2,则R为交换环。给出上述结果的一个简短证明,并将其推广,证明了定理:设R是具有正则元的半质环,如果R满足条件:对于任意的x,y∈R,都存在一个与x,y有关的整数n=n(x,y)≥1,使得(xy)n+k=yn+kxn+k,k=0,1,2,则R为交换环。Let R be an associative ring. The paper [1] gives the following result: Let R be a semi-prime ring with normal element, if R satisfies the condition: For Vx, y∈R, there is an integer n = n(x, y)≥1, related to x, y such that (xy)n+k = xn+kyn+k, k = 0, 1, 2, then R is commutative. An easier proof is presented of the above results. The results of the paper [1] are extened, the theorem is proved: Let R be a semi -prime ring with normal elements, if R satisfies the condition: For Vx, y∈R, there is an integer n = n(x, y)≥1, related to x, y, such that (xy)n+k = yn+kxn+k, k = 0, 1, 2, then R is commutative.

关 键 词：半质环 正则元 交换性 

分 类 号：O253.3[理学—数学]