Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Humio Ichimura

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Abstract

Let $\ell$ be a prime number, and $K$ a number field with $\zeta_{\ell} \in K^{\times}$. We give a simple necessary and sufficient condition for all tame Kummer extensions over $K$ of degree $\ell$ to have a relative normal integral basis. The result is given in terms of the class number and the group of units of $K$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 6 (2002), 76-79.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392678

Digital Object Identifier
doi:10.3792/pjaa.78.76

Mathematical Reviews number (MathSciNet)
MR1913934

Zentralblatt MATH identifier
1106.11308

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

Keywords
Normal integral basis Kummer extensions of prime degree

Citation

Ichimura, Humio. Note on the ring of integers of a Kummer extension of prime degree. V. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 6, 76--79. doi:10.3792/pjaa.78.76. https://projecteuclid.org/euclid.pja/1148392678


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References

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