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

Jean-Paul Cerri (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory

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.

Domaines: Théorie des nombres [math.NT]

Jean-Paul Cerri. Some Generalized Euclidean and 2-stage Euclidean number fields that are not norm-Euclidean. Mathematics of Computation, 2011, 80 (276), pp.2289-2298. ⟨hal-00505142v2⟩