Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on unramified quadratic extensions over algebraic number fields

Humio Ichimura

Full-text: Open access

Abstract

We construct for each integer $n$ ($\geq 3$), infinitely many number fields of degree $n$ each of which has an unramified quadratic extension with a power integral basis but no normal integral basis.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 5 (2000), 78-81.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393518

Digital Object Identifier
doi:10.3792/pjaa.76.78

Mathematical Reviews number (MathSciNet)
MR1771145

Zentralblatt MATH identifier
0958.11068

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

Keywords
Unramified quadratic extension power integral basis normal integral basis

Citation

Ichimura, Humio. A note on unramified quadratic extensions over algebraic number fields. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 5, 78--81. doi:10.3792/pjaa.76.78. https://projecteuclid.org/euclid.pja/1148393518


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References

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