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The Wedderburn Theorem

Published online by Cambridge University Press:  20 November 2018

Harry Goheen
Harry Goheen*
Affiliation:
Iowa State College
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Wedderburn, in 1905, proved that there are no finite skew-fields (5). Wedderburn's result has also been proved by Dickson, Artin, Witt, and Zassenhaus (2; 1; 6; 7); however, it seems to the author that the proofs so far given introduce concepts not obviously related to the theorem. It is the purpose of this note to use a result of Cartan, which was later proved in greater generality by Hua (4), to give a simpler and more direct version of the proof of Zassenhaus.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 60 - 62
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Artin, E., Ueber einen Satz von Herrn J. H. Maclagan-Wedderburn, Abh. Math. Sem. Univ. Hamburg, 5 (1927), 245–250.Google Scholar
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3. Frobenius, G., Ueber auflösbare Gruppen, IV, Berl. Ber., (1901), 1223–1225.Google Scholar
4. Hua, L. K., Some properties of a s field, Proc. Nat. Acad. Sci. U.S.A., 35 (1949), 533–537.Google Scholar
5. Maclagan-Wedderburn, J. H., A theorem on finite algebras, Trans. Amer. Math. Soc, 6 (1905), 349–352.Google Scholar
6. Witt, E., Ueber die Kommutativität endlicher Schiefkörper, Abh. Math. Sem. Univ. Hamburg, 8 (1930), 413.Google Scholar
7. Zassenhaus, H. J., A group-theoretic proof of a theorem of Maclagan-Wedderburn, Proc. Glasgow Math. Assoc, 1 (1952), 53–63.Google Scholar