On the Fueter model and monogeneity of rings of integers
type: Item
instance of: scholarly article
title: On the Fueter model and monogeneity of rings of integers
zbMATH Open document ID: 0778.11064
author: S. Singh
published in: Journal of Number Theory
publication date: 1993-05-16T00:00:00Z
review text: Let \(L/M\) be an extension of number fields. It is said that \(L\) is monogenic over \(M\) if \({\mathfrak D}_ L={\mathfrak D}_ M[\alpha]\) for some \(\alpha\in {\mathfrak D}_ L\), where \({\mathfrak D}_ L\) denotes the ring of integers in \(L\). Let \(K\) be an imaginary quadratic field in which 2 splits. For an integral ideal \({\mathfrak f}\) let \(K({\mathfrak f})\) denote the ray class field mod \({\mathfrak f}\). \textit{Ph. Cassou-Noguès} and \textit{M. J. Taylor} [J. Lond. Math. Soc., II. Ser. 37, 63--72 (1988; Zbl 0639.12001)] proved that \(K({\mathfrak f})\) is monogenic over \(K(1)\), the Hilbert class field, and gave a generator in terms of torsion values obtained from the Fueter model if \({\mathfrak f}\) is coprime to 2. In this paper the authors remove the condition that \({\mathfrak f}\) be coprime to 2. The proof uses the minimal Fueter model instead of the usual Fueter model. The minimal Fueter model has better properties about reduction modulo primes than the usual Fueter model, while the \(x\)-coordinates of both models coincide.
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 166056
zbMATH Keywords: monogeneity of rings of integers
zbMATH Keywords: extension
zbMATH Keywords: imaginary quadratic field
zbMATH Keywords: ray class field
zbMATH Keywords: generator
zbMATH Keywords: minimal Fueter model
MaRDI profile type: Publication
full work available at URL: jnth.1993.1005
OpenAlex ID: W2091030390
DOI: 10.1006/JNTH.1993.1005
description: scientific article; zbMATH DE number 166056