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On Conjugates in Division Rings

Published online by Cambridge University Press:  20 November 2018

Carl C. Faith
Carl C. Faith*
Affiliation:
The Pennsylvania State University
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Let D be a non-commutative division ring with centre C, and let Δ be a proper division subring not contained in C. In (4) Cartan raised the question: is it ever possible for each inner automorphism of D to induce an automorphism of Δ? As is well-known, Cartan (4, Théorème 4) with the aid of his Galois Theory answered this negatively in case D is a finite dimensional division algebra. Later Brauer (3), and Hua (8), using elegant, elementary methods, extended Cartan's theorem to arbitrary division rings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 374 - 380
Copyright
Copyright © Canadian Mathematical Society 1958

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