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On a Result of Faith

  • I. N. Herstein

Extract

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.

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References

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1. Brauer, Richard, On a theorem of H. Cartan, BAMS 55 (1949), 6. 9620.
2. Faith, Carl, Algebraic division ring extensions, PAMS 11 (1960), 4353.
3. Herstein, I. N., Two remarks on the commutativity of rings, Canadian Journal Math. 7 (1955), 411412.
4. Kaplansky, Irving, A theorem on division rings, Canadian Journal Math. 3 (1951), 290292.
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On a Result of Faith

  • I. N. Herstein

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