关于环的交换性定理的一个注记

A Note of Commutativity Theorem for Rings

设R是一个有单位元的结合环,证明了如下结果:若对于任意的a∈R\J(R),b∈R,满足(ab)k=akbk,其中k为3个连续的正整数,J(R)是R的Jacobson根,则R是一个交换环.

Let R be an associative ring with identity. It showed that for any a∈R／J（R）, b ∈R satisfied（ab）k = akbk , for three consecutive positive integers k, where J（R） was the Jacobson radical of R, then R was a commutative ring.