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Effective Field Theory and Algebraic Geometry

  • Michael D. Fried
  • Moshe Jarden
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 11)

Abstract

Present fashion in field theory and algebraic geometry is to replace classical constructive proofs by elegant existence proofs. For example, it is rare for students to see an actual procedure for factoring polynomials in ℚ [X 1, ... , X n ] in the course of finding out that it is a unique factorization domain. But constructive factorization is the essential backbone of constructive demonstrations that every K-algebraic set is the union of finitely many K-varieties (i.e., Hilbert’s basis theorem) and that every K-variety can be normalized.

Keywords

Algebraic Geometry Effective Field Theory Algebraic Closure Irreducible Factor Splitting Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. [FHJ]
    M. Fried, D. Haran and M. Jarden, Galois stratification over Frobenius fields, Advances in Mathematics 51 (1984), 1–35MathSciNetMATHCrossRefGoogle Scholar
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    B.L.v.d. Waerden, Modern Algebra 1,SpringerGoogle Scholar
  3. [W2]
    B.L.v.d. Waerden, Modern Algebra 2, SpringerGoogle Scholar
  4. [W3]
    A. Weil, L’arithmetique sur les courbes algébriques, Thèse, Paris 1928 = Acta Mathematica 52 (1928), 281–315MathSciNetCrossRefGoogle Scholar
  5. [L4]
    S. Lang, Introduction to Algebraic Geometry, Interscience Publishers, New York, 1964Google Scholar
  6. [ZS2]
    O. Zariski and P. Samuel, Commutative Algebra II, Springer, New York, 1960MATHGoogle Scholar
  7. [LLL]
    A.K. Lenstra, H.W. Lenstra Jr. and L. Lovâsz, Factoring polynomials with rational coefficients, Mathematische Annalen 261 (1982), 515–534MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Michael D. Fried
    • 1
  • Moshe Jarden
    • 2
  1. 1.Mathematical DepartmentUniversity of FloridaGainsvilleUSA
  2. 2.School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat Aviv, Tel AvivIsrael

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