Number Fields

1. Auflage 1977. Corr. 3rd printing 1995
ISBN: 978-0-387-90279-1
Verlag: Springer

Buch, Englisch, 292 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 910 g

Reihe: Universitext

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.

Zielgruppe

Graduate

Autoren/Hrsg.

Marcus, Daniel A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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 1: Commutative Rings and Ideals.- Appendix 2: Galois Theory for Subfields of C.- Appendix 3: Finite Fields and Rings.- Appendix 4: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.