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?
Why is every Archimedean ordered skew-field necessarily a field?
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$\begingroup$
field-theory
1 Answers
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This goes back to Hilbert. Here's his proof from Section 32 of Foundations of Geometry, 1902.