2011Mathematics of ComputationOpen access

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

Jean-Paul Cerri

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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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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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Available 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.

Key concepts: Euclidean geometry, Euclidean distance matrix, Mathematics, Euclidean distance, Euclidean domain, Euclidean group, Norm (philosophy), Combinatorics

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