数体（テキスト・第２版） Number Fields〈2nd ed. 2018〉

著者名：Marcus, Daniel A.

Springer（2018/07/05発売）

• 言語：ENG
• ISBN：9783319902326
• eISBN：9783319902333

Description

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 hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.

Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.

 

From the reviews:

“A thoroughly delightful introduction to algebraic number theory” – Ezra Brown in the Mathematical Reviews

“An excellent basis for an introductory graduate course in algebraic number theory” – Harold Edwards in the Bulletin of the American Mathematical Society

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.