# Additive commutators and the center of a division ring (2)

Can someone proof the following?
If $D$ is a division algebra over a field $F$, then as a $Z(D)$ algebra, $D$ is generated by the additive commutators (elements of the form $xy-yx$)

Thanks!

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Is it finite dimensional? – Myself Jan 13 '13 at 5:56
not necessarily – cruvadom Jan 13 '13 at 12:13