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On a Result of Faith

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein
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In a paper several years ago, Faith [2] proved an extension of a well-known theorem of Kaplansky [4]. His proof, even for the division ring case, was somewhat complicated. Using an old trick of Brauer [1] we show how Faith's theorem follows from Kaplansky's immediately.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 609
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Brauer, Richard, On a theorem of H. Cartan, BAMS 55 (1949), 6. 9–620.Google Scholar
2. Faith, Carl, Algebraic division ring extensions, PAMS 11 (1960), 43–53.Google Scholar
3. Herstein, I. N., Two remarks on the commutativity of rings, Canadian Journal Math. 7 (1955), 411–412.Google Scholar
4. Kaplansky, Irving, A theorem on division rings, Canadian Journal Math. 3 (1951), 290–292.Google Scholar