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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the Euclidean algorithm in quadratic number fields
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by H. Chatland PDF
Bull. Amer. Math. Soc. 55 (1949), 948-953
References
    1. P. G. L. Dirichlet, Vorlesungen über Zahlentheorie, ed. by R. Dirichlet, 4th ed., Braunschweig, 1894, p. 451. 2. L. E. Dickson, Algebren und ihre Zahlentheorie, Zürich and Leipzig, 1927, pp. 150-151. 3. O. Perron, Quadratische Zahlkörper mit Euklidischen Algorithmus, Math. Ann. vol. 107 (1932) pp. 489-495.
  • Alexander Oppenheim, Quadratic fields with and without Euclid’s algorithm, Math. Ann. 109 (1934), no. 1, 349–352. MR 1512898, DOI 10.1007/BF01449143
    • 5. R. Remak, Über den Euklidischen Algorithmus in reellquadratischen Zahlkörpern Jber. Deutschen Math. Verein. vol. 44 (1934) pp. 238-250.
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  • Nikolaus Hofreiter, Quadratische Zahlkörper ohne euklidischen Algorithmus, Math. Ann. 110 (1935), no. 1, 195–196 (German). MR 1512935, DOI 10.1007/BF01448024
    • 9. J. F. Keston, Existence of a Euclidean algorithm in quadratic fields, Thesis, Yale University, 1935; cf. Bull. Amer. Math. Soc. vol. 41 (1935) p. 186. 10. H. Behrbohm and L. Rédei, Dern Euklidische Algorithmus in quadratischen Körpern, J. Reine Angew. Math. vol. 174 (1935) pp. 192-205. 11. P. Erdös and Ch. Ko, Note on the Euclidean algorithm, J. London Math. Soc. vol. 13 (1938) pp. 3-8. 12. H. Heilbronn, On Euclid’s algorithm in real quadratic fields, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 521-526. 13. L. Schuster, Reelquadratische Zahlkörper ohne Euklidischen Algorithmus, Monatshefte für Mathematik und Physik vol. 47 (1938) pp. 117-127.
  • Alfred Brauer, On the non-existence of the Euclidean algorithm in certain quadratic number fields, Amer. J. Math. 62 (1940), 697–716. MR 2994, DOI 10.2307/2371480
  • L. Rédei, Zur Frage des Euklidischen Algorithmus in quadratischen Zahlkörpern, Math. Ann. 118 (1942), 588–608 (German). MR 10576, DOI 10.1007/BF01487388
  • Loo-Keng Hua and Szu-Hoa Min, On the distribution of quadratic non-residues and the Euclidean algorithm in real quadratic fields. II, Trans. Amer. Math. Soc. 56 (1944), 547–569. MR 11482, DOI 10.1090/S0002-9947-1944-0011482-1
  • L. K. Hua and W. T. Shih, On the lack of an Euclidean algorithm in $R(\sqrt {61})$, Amer. J. Math. 67 (1945), 209–211. MR 12091, DOI 10.2307/2371723
  • László Rédei, Über den Euklidschen Algorithmus in reell quadratischen Zahlkörpern, Mat. Fiz. Lapok 47 (1940), 78–90 (Hungarian, with German summary). MR 2355
  • H. Davenport, Indefinite binary quadratic forms, Quart. J. Math. Oxford Ser. (2) 1 (1950), 54–62. MR 34413, DOI 10.1093/qmath/1.1.54
Additional Information
  • Journal: Bull. Amer. Math. Soc. 55 (1949), 948-953
  • DOI: https://doi.org/10.1090/S0002-9904-1949-09315-1
  • MathSciNet review: 0031523