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Euclidean Rings of Algebraic Integers

Published online by Cambridge University Press:  20 November 2018

Malcolm Harper  and
M. Ram Murty
Malcolm Harper
Affiliation:
Champlain College, Montreal, Canada e-mail: malcolmharper@sympatico.ca
M. Ram Murty
Affiliation:
Department of Mathematics, Queen's University, Kingston, Ontario, K7L 3N6 e-mail: murty@mast.queensu.ca
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Abstract

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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.

Keywords

11R0411R2711R3211R4211N36

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 1 , 01 February 2004 , pp. 71 - 76
Copyright
Copyright © Canadian Mathematical Society 2004

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