Functiones et Approximatio Commentarii Mathematici

Euclidean algorithm in small Abelian fields

Władysław Narkiewicz

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Abstract

It is shown that a small change in the argument of Harper and Murty implies that there are at most two real quadratic fields with class-number one and without Euclidean algorithm.

Article information

Source
Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 337-340.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229619657

Digital Object Identifier
doi:10.7169/facm/1229619657

Mathematical Reviews number (MathSciNet)
MR2363830

Zentralblatt MATH identifier
1151.11349

Subjects
Primary: 11R11: Quadratic extensions
Secondary: 11R20: Other abelian and metabelian extensions 13F07: Euclidean rings and generalizations

Keywords
Euclidean algorithm real quadratic fields Abelian cubic fields

Citation

Narkiewicz, Władysław. Euclidean algorithm in small Abelian fields. Funct. Approx. Comment. Math. 37 (2007), no. 2, 337--340. doi:10.7169/facm/1229619657. https://projecteuclid.org/euclid.facm/1229619657


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References

  • M. Harper, $\bf Z[\sqrt14]$ is Euclidean, Canad. Math. J., 56, 2004, 55--70.
  • M. Harper, M.Ram Murty, Euclidean rings of algebraic integers, Canad. Math. J., 56, 2004, 71--76.
  • W. Narkiewicz, Units in residue classes, Arch. Math., 51, 1988, 238--241.
  • W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, 3rd ed., Springer 2004.
  • P.J. Weinberger, On Euclidean rings of algebraic integers, Proc. Symposia Pure Math., 24, 1972, 321--332.