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A Theorem Concerning Three Fields

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein
I. N. Herstein*
Affiliation:
University of Pennsylvania
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Several authors (1; 2; 3; 4; 5; 6) have recently studied the existence and non-existence of certain types of extensions of a given field. In this note we prove a theorem closely related to these results which, in a sense, contains essential portions of each of these.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 202 - 203
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Herstein, I. N., The structure of a certain class of rings, Amer. J. Math., 75 (1953), 864–871.Google Scholar
2. Ikeda, M., On a theorem of Kaplansky, Osaka Math. J., 4 (1952), 235–240.Google Scholar
3. Kaplansky, I., A theorem on division rings, Can. J. Math., 8 (1951), 290–292.Google Scholar
4. Krasner, M., The non-existence of certain extensions, Amer. J. Math., 75 (1953), 112–116.Google Scholar
5. Nagata, M., Nakayama, T., and Tuzuku, T., On an existence lemma in valuation theory, Nagoya Math. J., 6 (1953), 59–61.Google Scholar
6. Nakayama, T., The commutativity of division rings, Can. J. Math., 5 (1953), 242–244.Google Scholar