Proceedings of the Japan Academy, Series A, Mathematical Sciences

Note on the ring of integers of a Kummer extension of prime degree. II

Humio Ichimura

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Let $p$ be a prime number, and $a$ $(\in \mathbf{Q}^{\times})$ a rational number. Then, F. Kawamoto proved that the cyclic extension $\mathbf{Q}(\zeta_p, a^{1/p})/\mathbf{Q}(\zeta_p)$ has a normal integral basis if it is at most tamely ramified. We give some generalized version of this result replacing the base field $\mathbf{Q}$ with some real abelian fields of prime power conductor.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 2 (2001), 25-28.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

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

Normal integral basis tame extension Kummer extension of prime degree


Ichimura, Humio. Note on the ring of integers of a Kummer extension of prime degree. II. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 2, 25--28. doi:10.3792/pjaa.77.25.

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