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Ideal Theory

  • Emil Grosswald
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

As seen in Chapter 10, there are infinitely many algebraic number fields in which the uniqueness of factorization of integers fails (it is not known whether there are infinitely many fields with uniqueness of factorization). As already mentioned, of the two approaches to remedy the situation, the introduction of ideals has proved extremely successful while the continued extension of fields led to a certain disappointment (infinite class field towers). For this reason, we here interrupt the study of algebraic number fields, to develop the theory of ideals in rings of algebraic integers.

Keywords

Prime Ideal Ideal Theory Algebraic Number Class Number Principal Ideal 
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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Bibliography

  1. 1.
    E. Landau, Vorlesungen über Zahlentheorie, Vol. 3. Leipzig: S. Hirzel, 1927.MATHGoogle Scholar
  2. 2.
    N. H. McCoy, Rings and Ideals (Cams Monograph No. 8). La Salle, Illinois: Open Court, 1948.MATHGoogle Scholar
  3. 3.
    D. G. Northcott, Ideal Theory. Cambridge: Cambridge University Press, 1953.CrossRefMATHGoogle Scholar
  4. 4.
    H. Pollard, The Theory of Algebraic Numbers (Cams Monograph No. 9). New York: Wiley, 1950.MATHGoogle Scholar
  5. 5.
    E. Weiss, Algebraic Number Theory. New York: McGraw-Hill, 1963.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Emil Grosswald
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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