Re: linear algebra
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Homework assignment: prove that every finite integral domain is a field.
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Harder: Prove that every finite division ring is a field. [img]/images/graemlins/grin.gif[/img]
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Proof by citation: Wedderburn, 1905. [img]/images/graemlins/wink.gif[/img]
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I'm still mystified every time I think about this result. Finiteness => commutativity. It's absurd when you think about it. There is a truly beautiful proof of this result in Proofs from the Book.
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