# Division ring which is algebraic over $\mathbb R$

I am looking for the proof of the following

Theorem. If $L$ is a division ring algebraic over $\mathbb R$, then $L$ is $\mathbb R$-isomorphic to $\mathbb R$ or $\mathbb C$ or $\mathbb H$ , where $\mathbb H$ is a field of quaternions and $\mathbb C$ as usual the field of complex numbers.

Thanks.

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–  Ricky Demer Feb 12 '13 at 19:16