Non-principal Euclidean ideal class in a family of biquadratic fields with the class number two

DOI10.1007/s00013-022-01817-yOpenAlexW4319879272MaRDI QIDQ2697448

Sunil Kumar Pasupulati, Srilakshmi Krishnamoorthy

Publication date: 12 April 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.06464

zbMATH Keywords

Hilbert class fieldideal class groupArtin symbolEuclidean ideal classeuclidean algorithm for number fields

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Uses Software

• SageMath

Cites Work

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• The least prime quadratic nonresidue in a prescribed residue class mod 4
• On Euclidean ideal classes in certain abelian extensions
• Unramified extensions over low degree number fields
• Biquadratic fields having a non-principal Euclidean ideal class
• Growth results and Euclidean ideals
• Quadratic residues of certain types
• Two classes of number fields with a non-principal Euclidean ideal
• A family of number fields with unit rank at least 4 that has Euclidean ideals
• EXAMPLES OF NORM-EUCLIDEAN IDEAL CLASSES
• $\mathbb{Q}(\sqrt{2}, \sqrt{35})$ HAS A NON-PRINCIPAL EUCLIDEAN IDEAL

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