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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Some generalized Euclidean and $2$-stage Euclidean number fields that are not norm-Euclidean
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by Jean-Paul Cerri PDF
Math. Comp. 80 (2011), 2289-2298 Request permission


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:
  • Received by editor(s): September 11, 2009
  • Received by editor(s) in revised form: July 21, 2010
  • Published electronically: February 4, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 2289-2298
  • MSC (2010): Primary 11Y40; Secondary 11R04, 12J15, 13F07
  • DOI:
  • MathSciNet review: 2813361