The Kronecker-Vahlen theorem fails in real quadratic norm-Euclidean fields

DOI10.1016/j.jsc.2020.04.009zbMath1461.11144OpenAlexW3022695216WikidataQ114154463 ScholiaQ114154463MaRDI QIDQ2229704

Maksim Vaskouski, Nikita Kondratyonok

Publication date: 18 February 2021

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2020.04.009

zbMATH Keywords

Euclidean minimumdivision chainnorm-Euclidean quadratic number field

Mathematics Subject Classification ID

Quadratic extensions (11R11) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Cites Work

• Shortest division chains in unique factorization domains
• On the number of divisions of the Euclidean algorithm applied to Gaussian integers
• Shortest division chains in imaginary quadratic number fields
• On the construction of division chains in algebraic number rings,with applications to SL₂
• Computation of the Euclidean minimum of algebraic number fields
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