Dihedral algebras are cyclic

Authors:
Pascal Mammone and Jean-Pierre Tignol

Journal:
Proc. Amer. Math. Soc. **101** (1987), 217-218

MSC:
Primary 12E15; Secondary 16A39, 19C30

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902530-6

MathSciNet review:
902530

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Abstract | References | Similar Articles | Additional Information

Abstract: This note gives a simple proof of the following theorem of Rowen and Saltman: *Every central simple algebra split by a Galois extension of rank* ( *odd) with dihedral Galois group is cyclic if the center contains a primitive* *th root of unity*.

**[1]**A. A. Albert,*A note on normal division algebras of prime degree*, Bull. Amer. Math. Soc.**44**(1938), 649-652. MR**1563842****[2]**P. K. Draxl,*Skew fields*, London Math. Soc. Lecture Note Series 81, Cambridge Univ. Press, Cambridge, 1983. MR**696937 (85a:16022)****[3]**L. H. Rowen and D. J. Saltman,*Dihedral algebras are cyclic*, Proc. Amer. Math. Soc.**84**(1982), 162-164. MR**637160 (83c:16013)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902530-6

Keywords:
Central simple algebra,
cyclic algebra,
corestriction

Article copyright:
© Copyright 1987
American Mathematical Society