A note on unramified quadratic extensions over algebraic number fields

Humio Ichimura

doi:10.3792/pjaa.76.78

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May 2000 A note on unramified quadratic extensions over algebraic number fields

Humio Ichimura

Proc. Japan Acad. Ser. A Math. Sci. 76(5): 78-81 (May 2000). DOI: 10.3792/pjaa.76.78

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.

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Humio Ichimura. "A note on unramified quadratic extensions over algebraic number fields." Proc. Japan Acad. Ser. A Math. Sci. 76 (5) 78 - 81, May 2000. https://doi.org/10.3792/pjaa.76.78