Algebraic Number Theory

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


chapter we shall introduce the concept of an algebraic number field and develop its basic properties. Our treatment will be classical, developing directly only those aspects that will be needed in subsequent chapters. The study of these fields, and their interaction with other branches of mathematics forms a vast area of current research. Our objective is to develop as much of the general theory as is needed to study higher-power reciprocity. The reader who is interested in a more systematic treatment of these fields should consult any one of the standard texts on this subject, e.g., Ribenboim [207], Lang [168], Goldstein [140], Marcus [183].


Prime Ideal Galois Group Number Field Algebraic Number Galois Extension 
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 1982

Authors and Affiliations

  • Kenneth Ireland
    • 1
  • Michael Rosen
    • 2
  1. 1.Department of MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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