Euclidean algorithm in small Abelian fields

Władysław Narkiewicz

doi:10.7169/facm/1229619657

September 2007 Euclidean algorithm in small Abelian fields

Władysław Narkiewicz

Funct. Approx. Comment. Math. 37(2): 337-340 (September 2007). DOI: 10.7169/facm/1229619657

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.

References

1.

M. Harper, $\bf Z[\sqrt14]$ is Euclidean, Canad. Math. J., 56, 2004, 55--70. MR2031122 M. Harper, $\bf Z[\sqrt14]$ is Euclidean, Canad. Math. J., 56, 2004, 55--70. MR2031122

2.

M. Harper, M.Ram Murty, Euclidean rings of algebraic integers, Canad. Math. J., 56, 2004, 71--76. MR2031123 M. Harper, M.Ram Murty, Euclidean rings of algebraic integers, Canad. Math. J., 56, 2004, 71--76. MR2031123

3.

W. Narkiewicz, Units in residue classes, Arch. Math., 51, 1988, 238--241. MR960401 0641.12004 10.1007/BF01207477 W. Narkiewicz, Units in residue classes, Arch. Math., 51, 1988, 238--241. MR960401 0641.12004 10.1007/BF01207477

4.

W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, 3rd ed., Springer 2004. MR2078267 W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, 3rd ed., Springer 2004. MR2078267

5.

P.J. Weinberger, On Euclidean rings of algebraic integers, Proc. Symposia Pure Math., 24, 1972, 321--332. MR337902 0287.12012 P.J. Weinberger, On Euclidean rings of algebraic integers, Proc. Symposia Pure Math., 24, 1972, 321--332. MR337902 0287.12012

Citation Download Citation

Władysław Narkiewicz "Euclidean algorithm in small Abelian fields," Functiones et Approximatio Commentarii Mathematici 37(2), 337-340, (September 2007). https://doi.org/10.7169/facm/1229619657

Published: September 2007

Access the abstract

JOURNAL ARTICLE
4 PAGES

DOWNLOAD PDF + SAVE TO MY LIBRARY