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While browsing around, I read that any ordered skew-field that satisfies the Archimedean property is commutative, but it was offered without proof. Out of curiosity, is there a quick proof or reference for this fact?

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up vote 4 down vote accepted

This goes back to Hilbert. Here's his proof from Section 32 of Foundations of Geometry, 1902.

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Thank you, Bill. –  Dom Apr 6 '11 at 7:34

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