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 | References | Similar Articles | Additional Information

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. Adrian Albert,*Structure of algebras*, Revised printing. American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. MR**0123587****[2]**A. A. Albert,*A note on normal division algebras of prime degree*, Bull. Amer. Math. Soc.**44**(1938), no. 10, 649–652. MR**1563842**, https://doi.org/10.1090/S0002-9904-1938-06831-0**[3]**Nathan Jacobson,*Basic algebra. I*, W. H. Freeman and Co., San Francisco, Calif., 1974. MR**0356989****[4]**Robert L. Snider,*Is the Brauer group generated by cyclic algebras?*, Ring theory (Proc. Conf., Univ. Waterloo, Waterloo, 1978) Lecture Notes in Math., vol. 734, Springer, Berlin, 1979, pp. 279–301. MR**548134**

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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