Proceedings of the Japan Academy, Series A, Mathematical Sciences

Note on Galois descent of a normal integral basis of acyclic extension of degree p

Humio Ichimura

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 85, Number 10 (2009), 160-162.

Dates
First available in Project Euclid: 2 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.pja/1259763076

Digital Object Identifier
doi:10.3792/pjaa.85.160

Mathematical Reviews number (MathSciNet)
MR2591360

Zentralblatt MATH identifier
1232.11119

Subjects
Primary: 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]

Keywords
Normal integral basis locally free class group

Citation

Ichimura, Humio. Note on Galois descent of a normal integral basis of acyclic extension of degree p. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 10, 160--162. doi:10.3792/pjaa.85.160. https://projecteuclid.org/euclid.pja/1259763076


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