Euclidean Ideals in Quadratic Imaginary Fields

2009/09/14 by Graves, Hester, Ramsey, Nick
#11R04 #11R11 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0909.2593

Abstract

We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.

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• Biquadratic fields having a non-principal euclidean ideal class
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• On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two
• Divisibility of the class numbers of imaginary quadratic fields