Number Fields

2. Auflage 2018
ISBN: 978-3-319-90232-6
Verlag: Springer International Publishing

Buch, Englisch, 203 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 347 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 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.

Über Autor(innen)

Daniel A. Marcus received his PhD from Harvard University in 1972. He was a J. Willard Gibbs Instructor at Yale University from 1972 to 1974 and Professor of Mathematics at California State Polytechnic University, Pomona, from 1979 to 2004. He published research papers in the areas of graph theory, number theory and combinatorics. The present book grew out of a lecture course given by the author at Yale University.