Journal of the Mathematical Society of Japan

Hilbert-Speiser number fields and the complex conjugation

Humio ICHIMURA

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Abstract

Let p be a prime number. We say that a number field F satisfies the condition ( H p ) when any tame cyclic extension N / F of degree p has a normal integral basis. We determine all the CM Galois extensions F / Q satisfying ( H p ) for the case p 5 , using the action of the complex conjugation on several objects associated to F .

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 1 (2010), 83-94.

Dates
First available in Project Euclid: 5 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1265380425

Digital Object Identifier
doi:10.2969/jmsj/06210083

Mathematical Reviews number (MathSciNet)
MR2648217

Zentralblatt MATH identifier
1247.11142

Subjects
Primary: 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
Secondary: 11R18: Cyclotomic extensions

Keywords
Hilbert-Speiser number field normal integral basis CM field

Citation

ICHIMURA, Humio. Hilbert-Speiser number fields and the complex conjugation. J. Math. Soc. Japan 62 (2010), no. 1, 83--94. doi:10.2969/jmsj/06210083. https://projecteuclid.org/euclid.jmsj/1265380425


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