Submission: 2002, Dec 5, revised 2003, Apr 23
Wedderburn's first proof of his theorem on finite division algebras contains a gap. We analyse the gap, give a variant of Wedderburn's proof that goes completely without the gap-producing statement, and we show how to fill the gap in a way Wedderburn could probably have done it.
2000 Mathematics Subject Classification: 16K20, 12E20; 16K50
Keywords and Phrases: finite dimensional division algebras, finite fields, Brauer groups
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