Non-norm-Euclidean fields in basic \(Z_{l}\)-extensions

DOI10.3792/PJAA.92.23zbMath1415.11153OpenAlexW2210713291MaRDI QIDQ288542

Kuniaki Horie, Mitsuko Horie

Publication date: 27 May 2016

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1451330563

zbMATH Keywords

class numbercyclic fieldbasic \(Z_{l}\)-extensiongenus numbernorm-Euclidean field

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Other abelian and metabelian extensions (11R20)

Cites Work

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• The \(l\)-class group of the \(\mathbb Z_p\)-extension over the rational field
• Class numbers in cyclotomic \(\mathbb{Z}_p\)-extensions
• Numerische Bestimmung von Klassenzahlen reeller zyklischer Zahlkörper
• Sur la théorie du corps de classes sur le corps des nombres rationnels
• NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE
• Use of a Computer Scan to Prove Q (√2 + √2) and Q (√3 + √2) are Euclidean
• The Determination of the Imaginary Abelian Number Fields with Class Number One
• Class Number Computations of Real Abelian Number Fields
• The Genus Field and Genus Number in Algebraic Number Fields
• On Euclid's Algorithm in Cyclic Fields
• Zur Geschlechtertheorie in abelschen Zahlkörpern
• On the norm-Euclideanity of \(\mathbb Q\left(\sqrt{2+\sqrt{2+\sqrt 2}}\right)\) and \(\mathbb Q\left(\sqrt{2+\sqrt 2}\right)\)

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