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Mathematics of Computation

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Some generalized Euclidean and $ 2$-stage Euclidean number fields that are not norm-Euclidean


Author: Jean-Paul Cerri
Journal: Math. Comp. 80 (2011), 2289-2298
MSC (2010): Primary 11Y40; Secondary 11R04, 12J15, 13F07
DOI: https://doi.org/10.1090/S0025-5718-2011-02468-3
Published electronically: February 4, 2011
Supplement: Table supplement to this article.
MathSciNet review: 2813361
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Abstract: We give examples of Generalized Euclidean but not norm-Euclidean number fields of degree greater than 2. In the same way we give examples of 2-stage Euclidean but not norm-Euclidean number fields of degree greater than 2. In both cases, no such examples were known.


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Additional Information

Jean-Paul Cerri
Affiliation: IMB, 351, cours de la Libération, 33400 Talence, France
Email: Jean-Paul.Cerri@math.u-bordeaux1.fr

DOI: https://doi.org/10.1090/S0025-5718-2011-02468-3
Received by editor(s): September 11, 2009
Received by editor(s) in revised form: July 21, 2010
Published electronically: February 4, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.