CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Euclidean Rings of Algebraic Integers

  Published:2004-02-01
 Printed: Feb 2004
  • Malcolm Harper
  • M. Ram Murty
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Let $K$ be a finite Galois extension of the field of rational numbers with unit rank greater than~3. We prove that the ring of integers of $K$ is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions. We now prove this unconditionally.
MSC Classifications: 11R04, 11R27, 11R32, 11R42, 11N36 show english descriptions Algebraic numbers; rings of algebraic integers
Units and factorization
Galois theory
Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Applications of sieve methods
11R04 - Algebraic numbers; rings of algebraic integers
11R27 - Units and factorization
11R32 - Galois theory
11R42 - Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
11N36 - Applications of sieve methods
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/