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Journal Articles International Journal of Number Theory Year : 2012

Examples of norm-Euclidean ideal classes

Abstract

In 1978, Lenstra defined the notion of Euclidean ideal class. Using a slight modification of an algorithm computing the Euclidean minimum, we give new examples of number fields with norm-Euclidean ideal classes. Extending the results of Cioffari, we also establish the complete list of pure cubic number fields which admit a norm-Euclidean ideal class.
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Dates and versions

hal-00634643 , version 1 (21-10-2011)
hal-00634643 , version 2 (24-01-2012)

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Pierre Lezowski. Examples of norm-Euclidean ideal classes. International Journal of Number Theory, 2012, 8 (5), pp.1315-1333. ⟨10.1142/S1793042112500777⟩. ⟨hal-00634643v2⟩
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