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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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en.wikipedia.org/wiki/… $\:$ – Ricky Demer Feb 12 '13 at 19:16

One proof is in Hatcher's Algebraic Topology.

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any precise page number , if u know ? – Theorem Feb 12 '13 at 19:23
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@Theorem : pages 173, 222, 428. – DonAntonio Feb 12 '13 at 19:38

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