On power bases in cyclotomic number fields
type: Item
instance of: scholarly article
title: On power bases in cyclotomic number fields
zbMATH Open document ID: 0637.12001
DOI: 10.1016/0022-314X(88)90044-3
author: Andrew Bremner
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let p be an odd prime, and \(\zeta^ p=1\neq \zeta\). The author shows that \({\mathbb{Z}}[\zeta]={\mathbb{Z}}[\alpha]\) for \(\alpha =\zeta +\zeta^ 2+...+\zeta^{(p-1)/2}\), and conjectures that every integral generator of the ring \({\mathbb{Z}}[\zeta]\) is of the form \(m\pm \zeta^{\sigma}\) or \(m\pm \alpha^{\sigma}\), where \(m\in {\mathbb{Z}}\) and \(\sigma\) is an automorphism of \({\mathbb{Q}}(\zeta)\). The conjecture is proved to be true for \(p=7\).
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R18
zbMATH DE Number: 4037945
zbMATH Keywords: ring of cyclotomic integers
zbMATH Keywords: integral generator
reviewed by: Veikko Ennola
MaRDI profile type: Publication
cites work: Integral generators in a certain quartic field and related diophantine equations
cites work: Q4126428
cites work: On the representation of integers by binary cubic forms of positive discriminant
cites work: Q4124912
cites work: Sur les discriminants des nombres algébriques
cites work: Q3943047
description: scientific article; zbMATH DE number 4037945