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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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.

 

Factorization of prime ideal extensions in number rings
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by Ilaria Del Corso PDF
Math. Comp. 58 (1992), 849-853 Request permission

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
    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. L. Kronecker, Grundzüge einer arithmetischen Theorie der algebraischen Grössen, J. Reine Angew. Math. 92 (1882), 1-122; Werke 2, 237-387.
  • Serge Lang, Algebra, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1984. MR 783636
  • Daniel A. Marcus, Number fields, Universitext, Springer-Verlag, New York-Heidelberg, 1977. MR 0457396
  • Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 849-853
  • MSC: Primary 11R27; Secondary 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1122062-2
  • MathSciNet review: 1122062