On the norm-Euclideanity of \(\mathbb Q\left(\sqrt{2+\sqrt{2+\sqrt 2}}\right)\) and \(\mathbb Q\left(\sqrt{2+\sqrt 2}\right)\)

DOI10.5802/jtnb.269zbMath1014.11064OpenAlexW2531453584MaRDI QIDQ5939699

Jean-Paul Cerri

Publication date: 30 July 2001

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2000__12_1_103_0

zbMATH Keywords

Euclidean fieldsnorm-Euclideanity

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Cyclotomic extensions (11R18) Euclidean rings and generalizations (13F07)

Related Items (3)

Non-norm-Euclidean fields in basic \(Z_{l}\)-extensions ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ Euclidean minima of totally real number fields: Algorithmic determination

Cites Work

• The Euclidean algorithm in algebraic number fields
• A numerical study of Weber's real class number calculation
• Use of a Computer Scan to Prove Q (√2 + √2) and Q (√3 + √2) are Euclidean
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