Jacobson定理的推广

A Generalization of Jacobsons Theorem

1957年Herstein将著名的Jacobson定理推广为:如果对环R中任意元素x,y,均存在自然数n(x,y,)>1,使[x,y,]n(x,y)=[x,y],则R为交换环.本文证明了结合环的一个交换性定理,该定理与Herstein定理相平行,并由此推广了Jacobson定理.

Herstein generalized Jacobson's famous theorem in 1957 as following: Let R be a ring, if for every x, y∈R, there existed an integer n (x, y) >1 such that [x, y]n(x,y) = [x, y], then R is commutative. This paper proved a parallel theorem of Herstein on commutativity of associative rings, and used it to generalize a theorem of Jacobson.