# Which and where is the Periodicity Theorem of Jacobson?

I have this problem:

Prove that if $R$ is a ring such that all its subrings are division rings, then $R$ must be a field.

The problem is that the suggestion is to use the Periocidity theorem of Jacobson, but I don't find it by that name. Can anyone say me which theorem could be the one that is reffered as the suggestion and in which book find it?

If $R$ is a ring such that for every $x\in R$ there exists a natural number $n$ such that $x^n=x$, then $R$ is commutative.