Geodesic
A Note on Division Algebras
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 734-736

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Herstein, I. N.; Ramer, A. A Note on Division Algebras. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 734-736. doi: 10.4153/CJM-1972-069-4
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[1] 1. Artin, E., Galois theory (Notre Dame Mathematical Lectures No. 2, 1946). Google Scholar

[2] 2. Herstein, I. N., Non-commutative rings (Carus Monograph No. 15, 1968). Google Scholar

[3] 3. Nathan, Jacobson, Structure of rings (A.M.S. Colloquium Series, No. XXXVII, 1956, 1964). Google Scholar

[4] 4. Irving, Kaplansky, Fields and rings (Chicago Lectures in Mathematics, 1969). Google Scholar

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