Number Fields

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several...

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Bibliographische Detailangaben
1. Verfasser: Marcus, Daniel A. (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:2nd ed. 2018.
Schriftenreihe:Universitext,
Schlagworte:
Number theory.
Algebra.
ISBN:9783319902333
ISSN:0172-5939
Online-Zugang: Volltext
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Inhaltsangabe:
  • 1: A Special Case of Fermat's Conjecture
  • 2: Number Fields and Number Rings
  • 3: Prime Decomposition in Number Rings
  • 4: Galois Theory Applied to Prime Decomposition
  • 5: The Ideal Class Group and the Unit Group
  • 6: The Distribution of Ideals in a Number Ring
  • 7: The Dedekind Zeta Function and the Class Number Formula
  • 8: The Distribution of Primes and an Introduction to Class Field Theory
  • Appendix A: Commutative Rings and Ideals
  • Appendix B: Galois Theory for Subfields of C
  • Appendix C: Finite Fields and Rings
  • Appendix D: Two Pages of Primes
  • Further Reading
  • Index of Theorems
  • List of Symbols.

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