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December 2009 Note on Galois descent of a normal integral basis of acyclic extension of degree p
Humio Ichimura
Proc. Japan Acad. Ser. A Math. Sci. 85(10): 160-162 (December 2009). DOI: 10.3792/pjaa.85.160

Abstract

Let p be an odd prime number, and F a number field. We show that when F/Q is unramified at p, any tame cyclic extension N/F of degree p has a normal integral basis if the pushed up extension $N(\zeta_p)/F(\zeta_p)$ has a normal integral basis.

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Humio Ichimura. "Note on Galois descent of a normal integral basis of acyclic extension of degree p." Proc. Japan Acad. Ser. A Math. Sci. 85 (10) 160 - 162, December 2009. https://doi.org/10.3792/pjaa.85.160

Information

Published: December 2009
First available in Project Euclid: 2 December 2009

zbMATH: 1232.11119
MathSciNet: MR2591360
Digital Object Identifier: 10.3792/pjaa.85.160

Subjects:
Primary: 11R33

Keywords: locally free class group , normal integral basis

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 10 • December 2009
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