I'm reading a paper of Maurice Chacron and I.N. Herstein entitled Powers of skew and symmetric elements in division rings.
At the first page of the paper, I got stuck in a problem that:
"if in a division ring $R$, $a^{m}b^{n}=b^{n}a^{m}$, for all $a, b \in R$, and appropriate $m,n >0$ depending on $a,b$, then $R$ is a field".
Is this a right statement? Thanks for helping me!