Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

The Euclidean condition in pure cubic and complex quartic fields


Author: Vincent G. Cioffari
Journal: Math. Comp. 33 (1979), 389-398
MSC: Primary 12A30
MathSciNet review: 514835
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that a field $ Q{(^3}\sqrt d )$ is euclidean with respect to the ordinary norm if and only if $ d = 2,3$ or 10. We also prove that certain fields of the form $ Q{(^4}\sqrt { - d} ),d > 0$, are or are not euclidean.


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

  • [1] J. W. S. Cassels, The inhomogeneous minimum of binary quadratic, ternary cubic and quaternary quartic forms, Proc. Cambridge Philos. Soc. 48 (1952), 72–86. MR 0047709
  • [2] H. C. WILLIAMS, From a computer print-out, done recently at the University of Manitoba.
  • [3] H. J. Godwin, On Euclid’s algorithm in some cubic fields with signature one, Quart. J. Math. Oxford Ser. (2) 18 (1967), 333–338. MR 0219509
  • [4] Elizabeth M. Taylor, Euclid’s algorithm in cubic fields with complex conjugates, J. London Math. Soc. (2) 14 (1976), no. 1, 49–54. MR 0419399
  • [5] C. CHEVALLEY, C. R. Acad. Sci. Paris, v. 192, 1931, pp. 257-258.
  • [6] Richard B. Lakein, Euclid’s algorithm in complex quartic fields, Acta Arith. 20 (1972), 393–400. MR 0304350

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A30

Retrieve articles in all journals with MSC: 12A30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0514835-5
Article copyright: © Copyright 1979 American Mathematical Society