Abelian Groups in Rational Number Theory

  • Erich Hecke
Part of the Graduate Texts in Mathematics book series (GTM, volume 77)


In the elementary theory of rational numbers we are constantly dealing with Abelian groups. The set of integers has the properties:
  1. (i)

    a + b is an integer if a and b are integers; a + b = b + a,

  2. (ii)

    a + (b + c) = (a + b) + c,

  3. (iii)

    If a + b = a′ + b, then a = a′,

  4. (iv)

    For each a and b there is an integer x such that a + x = b.



Abelian Group Residue Class Quadratic Residue Residue Character Residue Symbol 
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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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Erich Hecke
    • 1
  1. 1.Department of MathematicsUniversität HamburgHamburgFederal Republic of Germany

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