Number Fields

• Main Author: Marcus, Daniel A. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Universitext,
• Subjects: Number theory.; Algebra.; Number Theory.

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...

Table of Contents:

• 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.