Dihedral algebras are cyclic
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- by Pascal Mammone and Jean-Pierre Tignol PDF
- Proc. Amer. Math. Soc. 101 (1987), 217-218 Request permission
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 $2n$ ($n$ odd) with dihedral Galois group is cyclic if the center contains a primitive $n$th root of unity.References
- A. A. Albert, A note on normal division algebras of prime degree, Bull. Amer. Math. Soc. 44 (1938), no. 10, 649–652. MR 1563842, DOI 10.1090/S0002-9904-1938-06831-0
- P. K. Draxl, Skew fields, London Mathematical Society Lecture Note Series, vol. 81, Cambridge University Press, Cambridge, 1983. MR 696937, DOI 10.1017/CBO9780511661907
- Louis H. Rowen and David J. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84 (1982), no. 2, 162–164. MR 637160, DOI 10.1090/S0002-9939-1982-0637160-2
Additional Information
- © Copyright 1987 American Mathematical Society
- 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