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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Metacyclic $ p$-algebras


Author: Ming Chang Kang
Journal: Proc. Amer. Math. Soc. 104 (1988), 697-698
MSC: Primary 16A39; Secondary 12E15, 19C30
MathSciNet review: 933515
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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].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0933515-2
PII: S 0002-9939(1988)0933515-2
Keywords: Central simple algebra, cyclic algebra
Article copyright: © Copyright 1988 American Mathematical Society