All dihedral division algebras of degree five are cyclic
Author:
Eliyahu Matzri
Journal:
Proc. Amer. Math. Soc. 136 (2008), 19251931
MSC (2000):
Primary 16K20, 12E15
Published electronically:
February 7, 2008
MathSciNet review:
2383498
Fulltext PDF Free Access
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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, BarIlan University, RamatGan, 52900, Israel
Email:
elimatzri@gmail.com
DOI:
http://dx.doi.org/10.1090/S0002993908093106
PII:
S 00029939(08)093106
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. 2004083.
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
