Units in residue classes
type: Item
instance of: scholarly article
title: Units in residue classes
zbMATH Open document ID: 0641.12004
DOI: 10.1007/BF01207477
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: It is shown that if \(K\neq {\mathbb{Q}}\) is a real Abelian field of degree \(>3\), then there exist infinitely many prime ideals P of first degree in K/\({\mathbb{Q}}\) such that every non-zero residue class (mod P) contains a unit. The same holds also for real quadratic and cubic Abelian fields with at most two exceptions.
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R44
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 4043960
zbMATH Keywords: real Abelian field
zbMATH Keywords: unit
author: Władysław Narkiewicz
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
cites work: On the construction of division chains in algebraic number rings,with applications to SL2
cites work: A remark on Artin's conjecture
cites work: ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS
cites work: On Artin's conjecture and Euclid's algorithm in global fields
cites work: A note on Artin's conjecture in algebraic number fields.
full work available at URL: https://doi.org/10.1007/bf01207477
OpenAlex ID: W1992572374
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description: scientific article; zbMATH DE number 4043960