The Euclidean algorithm for number fields and primitive roots
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- by M. R. Murty and Kathleen L. Petersen PDF
- Proc. Amer. Math. Soc. 141 (2013), 181-190 Request permission
Abstract:
Let $K$ be a number field with unit rank at least four, containing a subfield $M$ such that $K/M$ is Galois of degree at least four. We show 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 prove this unconditionally.References
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Additional Information
- M. R. Murty
- Affiliation: Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, University Avenue, Kingston, ON K7L 3N6, Canada
- MR Author ID: 128555
- Email: murty@mast.queensu.ca
- Kathleen L. Petersen
- Affiliation: Department of Mathematics, Florida State University, 208 Love Building, Tallahassee, Florida 32306
- MR Author ID: 811372
- Email: petersen@math.fsu.edu
- Received by editor(s): January 6, 2011
- Received by editor(s) in revised form: June 22, 2011
- Published electronically: May 25, 2012
- Communicated by: Matthew A. Papanikolas
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 181-190
- MSC (2010): Primary 11A07, 11N36
- DOI: https://doi.org/10.1090/S0002-9939-2012-11327-9
- MathSciNet review: 2988721