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A Note on Division Algebras

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein  and
A. Ramer
I. N. Herstein
Affiliation:
University of Chicago, Chicago, Illinois
A. Ramer
Affiliation:
Weizmann Institute of Science, Rehovot, Israel
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In this note we prove some results on the intersection properties of maximal subfields of division algebras which are finite dimensional over their centers. These results indicate that we can get very small intersections with any subalgebra if we use the appropriate maximal subfields. As a consequence of our first theorem, we obtain some theorems which are known and some which can be obtained from these known theorems (see, for instance, Theorem 3, Chapter VII in [3]). The proofs of these known results given here are very elementary and are quite different from the ones in the literature.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 734 - 736
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Artin, E., Galois theory (Notre Dame Mathematical Lectures No. 2, 1946).Google Scholar
2. Herstein, I. N., Non-commutative rings (Carus Monograph No. 15, 1968).Google Scholar
3. Nathan, Jacobson, Structure of rings (A.M.S. Colloquium Series, No. XXXVII, 1956, 1964).Google Scholar
4. Irving, Kaplansky, Fields and rings (Chicago Lectures in Mathematics, 1969).Google Scholar