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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Factorization of prime ideal extensions in number rings

Author: Ilaria Del Corso
Journal: Math. Comp. 58 (1992), 849-853
MSC: Primary 11R27; Secondary 11Y40
MathSciNet review: 1122062
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Abstract | References | Similar Articles | Additional Information

Abstract: Following an idea of Kronecker, we describe a method for factoring prime ideal extensions in number rings. The method needs factorization of polynomials in many variables over finite fields, but it works for any prime and any number field extension.

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

  • [1] K. Hensel, Untersuchung der Fundamentalgleichung einer Gattung für eine reelle Primzahl als Modul und Bestimmung der Theiler ihrer Discriminante, J. Reine Angew. Math. 113 (1894), 61-83.
  • [2] L. Kronecker, Grundzüge einer arithmetischen Theorie der algebraischen Grössen, J. Reine Angew. Math. 92 (1882), 1-122; Werke 2, 237-387.
  • [3] Serge Lang, Algebra, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1984. MR 783636 (86j:00003)
  • [4] Daniel A. Marcus, Number fields, Springer-Verlag, New York-Heidelberg, 1977. Universitext. MR 0457396 (56 #15601)
  • [5] Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830 (91h:11107)

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Additional Information

PII: S 0025-5718(1992)1122062-2
Article copyright: © Copyright 1992 American Mathematical Society

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