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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dihedral algebras are cyclic


Authors: Louis H. Rowen and David J. Saltman
Journal: Proc. Amer. Math. Soc. 84 (1982), 162-164
MSC: Primary 16A39; Secondary 12E15
MathSciNet review: 637160
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Abstract: Any central simple algebra of degree $ n$ split by a Galois extension with dihedral Galois group of degree $ 2n$ is, in fact, a cyclic algebra. We assume that the centers of these algebras contain a primitive $ n$th root of unity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637160-2
PII: S 0002-9939(1982)0637160-2
Keywords: Central simple algebra, cyclic algebra
Article copyright: © Copyright 1982 American Mathematical Society