Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On generalized quaternions


Author: Gordon Pall
Journal: Trans. Amer. Math. Soc. 59 (1946), 280-332
MSC: Primary 10.0X
DOI: https://doi.org/10.1090/S0002-9947-1946-0018702-X
MathSciNet review: 0018702
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] P. Bachmann, Die Arithmetik der quadratischen Formen, I, Leipzig, 1898.
  • [2] H. Brandt, Idealtheorie in Quaternionalgebren, Math. Ann. vol. 99 (1928) pp. 1-29. MR 1512436
  • [3] L. E. Dickson, (a) Algebras and their arithmetics, Chicago, 1923; (b) Algebren und ihre Zahlentheorie, Zürich, 1927; (c) Studies in the theory of numbers, Chicago, 1930.
  • [4] H. Hasse, Über die Äquivalenz quadratischer Formen in Körper der rationalen Zahlen, Journal für Mathematik vol. 152 (1923) pp. 205-224.
  • [5] K. Hensel, Zahlentheorie, Berlin and Leipzig, 1913.
  • [6] C. Hermite, (a) Sur la théorie des formes quadratiques, Journal für Mathematik vol. 47 (1854) pp. 307-342; (b) vol. 41 (1850) p. 192.
  • [7] A. Hurwitz, Vorlesungen über die Zahlentheorie der Quaternionen, Berlin, 1919.
  • [8] B. W. Jones and G. Pall, Regular and semi-regular positive ternary quadratic forms, Acta Math. vol. 70 (1939) pp. 165-191. MR 1555447
  • [9] A. Korkine and G. Zolotareff, Sur les formes quadratiques positives quaternaires, Math. Ann. vol. 5 (1872) pp. 581-583. MR 1509795
  • [10] C. G. Latimer, The classes of integral sets in a quaternion algebra, Duke Math. J. vol. 3 (1937) pp. 237-247. MR 1545983
  • [11] U. V. Linnik, (a) On certain results relating to positive tenrary quadratic forms, Rec. Math. (Mat. Sbornik) N.S. vol. 5 (1939) pp. 453-471; (b) Über die Darstellung grosser Zahlen durch positive ternäre quadratische Formen, Bull. Acad. Sci. URSS Sér. Math. vol. 4 (1940) pp. 363-402. MR 0002346 (2:36a)
  • [12] G. Pall, On the factorization of generalized quaternions, Duke Math. J. vol. 4 (1938) pp. 696-704. MR 1546090
  • [13] H. J. S. Smith, Collected mathematical papers, Oxford, 1894.
  • [14] S. B. Townes, Table of reduced positive quaternary quadratic forms, Ann. of Math. vol. 41 (1940) pp. 57-58. MR 0000830 (1:134g)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10.0X

Retrieve articles in all journals with MSC: 10.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1946-0018702-X
Article copyright: © Copyright 1946 American Mathematical Society

American Mathematical Society