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History of Field Theory

  • Israel Kleiner

Keywords

Riemann Surface Algebraic Geometry Prime Ideal Algebraic Number Algebraic Function 
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References

  1. 1.
    I. G. Bashmakova and E. I. Slavutin, Algebra and algebraic number theory, in Mathematics of the 19th Century, ed. by A. N. Kolmogorov and A. P. Yushkevich, Birkhäuser, 1992, pp. 35–135.Google Scholar
  2. 2.
    G. Birkhoff, Current trends in algebra, American Math. Monthly 1973, 80: 760–782, and corrections in 1974, 81: 746.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    N. Bourbaki, Elements of the History of Mathematics, Springer-Verlag, 1984.Google Scholar
  4. 4.
    L. Corry, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser, 1996.Google Scholar
  5. 5.
    H. M. Edwards, Fermat’s Last Theorem: A Genetic Introduction to Algebraic Number Theory, Springer-Verlag, 1977.Google Scholar
  6. 6.
    D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, 1995.Google Scholar
  7. 7.
    E. Galois, Sur la théorie des nombres. English translation in Introductory Modern Algebra: A Historical Approach, by S. Stahl, Wiley, 1997, pp. 277–284.Google Scholar
  8. 8.
    H. Hasse, History of class field theory, in Algebraic Number Theory, Proceedings of an Instructional Conference, ed. by J. Cassels & A. Fröhlich, Thompson Book Co., 1967, pp. 266–279.Google Scholar
  9. 9.
    K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1982.Google Scholar
  10. 10.
    N. Jacobson, Basic Algebra I, II, W. H. Freeman, 1974 & 1980.Google Scholar
  11. 11.
    B. M. Kiernan, The development of Galois theory from Lagrange to Artin, Arch. Hist. Ex. Sc. 1971/72, 8: 40–154.CrossRefMathSciNetGoogle Scholar
  12. 12.
    I. Kleiner, The roots of commutative algebra in algebraic number theory, Math. Mag. 1995, 68: 3–15.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    D. Laugwitz, Bernhard Riemann, 1826–1866, Birkhäuser, 1999. (Translated from the German by A. Shenitzer.)Google Scholar
  14. 14.
    R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications,Cambridge University Press, 1986.Google Scholar
  15. 15.
    E. H. Moore, A doubly-infinite system of simple groups, New York Math. Soc. Bull. 1893, 3: 73–78.CrossRefGoogle Scholar
  16. 16.
    W. Purkert, Zur Genesis des abstrakten Körperbegriffs I, II, NTM 1971, 8: 23–37 and 1973, 10: 8–20. (Unpublished English translation by A. Shenitzer.)Google Scholar
  17. 17.
    W. Purkert and H. Wussing, Abstract algebra, in Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, ed. by I. Grattan-Guinness, Routledge, 1994, vol. 1, pp. 741–760.Google Scholar
  18. 18.
    H. M. Pycior, George Peacock and the British origins of symbolical algebra, Hist. Math. 1981, 8: 23–45.CrossRefMathSciNetGoogle Scholar
  19. 19.
    J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer-Verlag, 1992.Google Scholar
  20. 20.
    E. Steinitz, Algebraische Theorie der Körper, 2nd ed., Chelsea, 1950.Google Scholar
  21. 21.
    J.-P. Tignol, Galois’ Theory of Algebraic Equations, Wiley, 1988.Google Scholar
  22. 22.
    B. L. van der Waerden, Die Algebra seit Galois, Jahresbericht d. DMV 1966, 68: 155–165.MATHGoogle Scholar
  23. 23.
    H. Weber, Die allgemeinen Grundlagen der Galois’schen Gleichungstheorie, Math. Ann. 1893, 43: 521–549.CrossRefMathSciNetGoogle Scholar
  24. 24.
    D. Winter, The Structure of Fields, Springer-Verlag, 1974.Google Scholar
  25. 25.
    M. Scanlan, Who were the American postulate theorists?, Jour. of Symbolic Logic 1991, 56: 981–1002.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Israel Kleiner
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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