On the unramified Kummer extensions of quadratic extensions of the prime cyclotomic number field
type: Item
instance of: scholarly article
title: On the unramified Kummer extensions of quadratic extensions of the prime cyclotomic number field
zbMATH Open document ID: 0728.11056
DOI: 10.1007/BF01199061
author: Norikata Nakagoshi
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: Let \(\ell\) be an odd prime and d be a square free rational integer, prime to \(\ell\). In this paper we give sufficient conditions to obtain the unramified Kummer extensions of \({\mathbb{Q}}(\exp (2\pi i/\ell), \sqrt{d}),\) of degree \(\ell\) or \(\ell^ 2\), using the \(\ell\)-th roots of the units of \({\mathbb{Q}}(\sqrt{(-1)^{(\ell -1)/2}\ell}, \sqrt{d}),\) when d is not a quadratic residue modulo \(\ell\). If d is a quadratic residue modulo \(\ell\), then sufficient conditions like these were already given in the previous paper [Nagoya Math. J. 115, 151-164 (1989; Zbl 0659.12007)].
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 4202402
zbMATH Keywords: unramified Kummer extensions
MaRDI profile type: Publication
cites work: The structure of the multiplicative group of residue classes modulo
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description: scientific article; zbMATH DE number 4202402