Proceedings of the Japan Academy, Series A, Mathematical Sciences

Normal integral basis and ray class group modulo 4

Humio Ichimura and Fuminori Kawamoto

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We prove that a number field $K$ satisfies the following property (B) if and only if the ray class group of $K$ defined modulo 4 is trivial. (B): For any tame abelian extensions $N_1$ and $N_2$ over $K$ of exponent 2, the composite $N_1N_2/K$ has a relative normal integral basis (NIB) if both $N_1/K$ and $N_2/K$ have a NIB.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 9 (2003), 139-141.

First available in Project Euclid: 18 May 2005

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

Normal integral basis ray class group


Ichimura, Humio; Kawamoto, Fuminori. Normal integral basis and ray class group modulo 4. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 9, 139--141. doi:10.3792/pjaa.79.139.

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