All dihedral division algebras of degree five are cyclic

Author:
Eliyahu Matzri

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1925-1931

MSC (2000):
Primary 16K20, 12E15

Published electronically:
February 7, 2008

MathSciNet review:
2383498

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Abstract: In 1982 Rowen and Saltman proved that every division algebra which is split by a dihedral extension of degree of the center, odd, is in fact cyclic. The proof requires roots of unity of order in the center. We show that for , this assumption can be removed. It then follows that , the -torsion part of the Brauer group, is generated by cyclic algebras, generalizing a result of Merkurjev (1983) on the and torsion parts.

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Additional Information

**Eliyahu Matzri**

Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

Email:
elimatzri@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-08-09310-6

Keywords:
Central simple algebras,
cyclic algebras

Received by editor(s):
November 27, 2006

Published electronically:
February 7, 2008

Additional Notes:
The author thanks his supervisors, L. H. Rowen and U. Vishne, for many interesting and motivating talks and for supporting this work through BSF grant no. 2004-083.

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.