Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1982-0637160-2
MathSciNet review: 637160
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] A. A. Albert, Structure of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R.I., 1939. MR 0123587 (23:A912)
  • [2] -, A note on normal division algebras of prime degree, Bull. Amer. Math. Soc. 44 (1938), 649-652. MR 1563842
  • [3] N. Jacobson, Basic algebra. I, Freeman, San Francisco, Calif., 1974. MR 0356989 (50:9457)
  • [4] R. Snider, Is the Brauer Group generated by cydies?, Ring Theory (Waterloo, 1978), (D. Handelman and J. Lawrence, Eds.), Lecture Notes in Math., vol. 734, Springer-Verlag, Berlin and New York, 1979. MR 548134 (80k:16010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A39, 12E15

Retrieve articles in all journals with MSC: 16A39, 12E15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637160-2
Keywords: Central simple algebra, cyclic algebra
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society