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

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Abstract: Any central simple algebra of degree split by a Galois extension with dihedral Galois group of degree is, in fact, a cyclic algebra. We assume that the centers of these algebras contain a primitive th root of unity.

**[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)**

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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