Metacyclic $p$-algebras
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- by Ming Chang Kang PDF
- Proc. Amer. Math. Soc. 104 (1988), 697-698 Request permission
Abstract:
Let $K$ be a field of char $K = p > 0,m,r$ any positive integers with $(p,m) = 1$, and $L$ a metacyclic extension of $K$ with degree ${p^r}m$, i.e. ${\text {Gal(}}L/K) = \left \langle {\sigma ,\tau :{\sigma ^{{p^r}}} = {\tau ^m} = 1,\tau \sigma {\tau ^{ - 1}} = {\sigma ^e}} \right \rangle$ for some integer $e$. If $A$ is a central simple $K$-algebra of degree ${p^r}$ and is split by $L$, then $A$ is a cyclic algebra. For $r = 1$, the theorem has been proved by A. A. Albert [1].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
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 697-698
- MSC: Primary 16A39; Secondary 12E15, 19C30
- DOI: https://doi.org/10.1090/S0002-9939-1988-0933515-2
- MathSciNet review: 933515