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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
2. Dickson, L. E., On finite algebras, Gött. Nachr. (1905), 358–393.Google Scholar
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