Biquadratic fields having a non-principal euclidean ideal class

2018/09/20 by Chattopadhyay, Jaitra, Muthukrishnan, Subramani · 2 citations
#11A05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.07478

Abstract

H. W. Lenstra \citelenstra introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number fields of small degree were obtained with an Euclidean ideal class (for instance, in \citehester1 and \citecathy). In this paper, we construct certain new families of biquadratic number fields having a non-principal Euclidean ideal class and this extends the previously known families given by H. Graves \citehester1 and C. Hsu \citecathy.

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• Euclidean Algorithms for Ideal Classes in Biquadratic fields: A Genus-Theoretic Perspective
• Absolutely Abelian Hilbert Class Fields and ℓ-torsion conjecture

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