ON A THEOREM OF YEN

Source abstract

In [5] Yen showed that if $R$ is an associative ring with unity and $m > 1$ is a fixed integer such that $m =2(\text{ mod } 4)$ and $(x +y)^m =x^m +y^m$ for all $x$, $y$ in $R$, then $R$ must be commutative. In the present paper it is shown that commutativity is achieved even in the case where $m$ is dependent on $x$ and $y$.