On the ring of integers of a tame Kummer extension over a number field.
type: Item
instance of: scholarly article
title: On the ring of integers of a tame Kummer extension over a number field.
zbMATH Open document ID: 1042.11074
DOI: 10.1016/S0022-4049(03)00148-8
author: Humio Ichimura
published in: Journal of Pure and Applied Algebra
publication date: 2004-02-02T00:00:00Z
review text: Let \(K/F\) be a finite Galois extension of number fields. Generalizing results of \textit{E. J. Gómez Ayala} [J. Théor. Nombres Bordx. 6, 95--116 (1994; Zbl 0822.11076)], the author characterizes tamely ramified cyclic Kummer extensions \(K/F\) with normal integral bases. As an application, he obtains the following capitulation result: given an integer \(m \geq 2\) and a number field \(F\) containing the \(m\)th roots of unity, there is a finite extension \(L/F\) such that for any abelian extension \(K/F\) with exponent \(m\), the extension \(LK/L\) has a normal integral basis.
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R33
zbMATH DE Number: 2035899
zbMATH Keywords: normal integral basis
zbMATH Keywords: Kummer extensions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2035899