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Classical Theory of Algebraic Numbers Paulo Ribenboim

Classical Theory of Algebraic Numbers By Paulo Ribenboim

Classical Theory of Algebraic Numbers by Paulo Ribenboim


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Summary

The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.

Classical Theory of Algebraic Numbers Summary

Classical Theory of Algebraic Numbers by Paulo Ribenboim

The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.

Classical Theory of Algebraic Numbers Reviews

From the reviews of the second edition:

This book is a thorough self-contained introduction to algebraic number theory. ... The book is aimed at graduate students. The author made a great effort to make the subject easier to understand. The proofs are very detailed, there are plenty of examples and there are exercises at the end of almost all chapters ... . The book contains a great amount of material, more than enough for a year-long course. (Gabor Megyesi, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

There is a wealth of material in this book. The approach is very classical and global. ... the author keeps his presentation self-contained. The author has made a real effort to make the book accessible to students. Proofs are given in great detail, and there are many examples and exercises. The book would serve well as a text for a graduate course in classical algebraic number theory. (Lawrence Washington, Mathematical Reviews, Issue 2002 e)

Ribenboims's 'Classical Theory of Algebraic Numbers' is an introduction to algebraic number theory on an elementary level ... . Ribenboim's book is a well written introduction to classical algebraic number theory ... and the perfect textbook for students who need lots of examples. (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1082, 2006)

Table of Contents

* Unique Factorization Domains, Ideals, Principal Ideal Domains * Commutative Fields * Residue Classes * Quadratic Residues * Algebraic Integers * Integral Basis, Discriminant * The Decomposition of Ideals * The Norm and Classes of Ideals * Estimates for the Discriminant * Units * Extension of Ideals * Algebraic Interlude * The Relative Trace, Norm, Discriminant and Different * The Decomposition of Prime Ideals in Galois Extensions * Complements and Miscellaneous Numerical Examples * Local Methods for Cyclotomic Fields * Bernoulli Numbers * Fermat's Last Theorem for Regular Prime Exponents * More on Cyclotomic Extensions * Characters and Gaussian Sums * Zeta-Functions and L-Series * The Dedekind Zeta- Function * Primes in Arithmetic Progressions * The Frobenius Automorphism and the Splitting of Prime Ideals * Class Number of Quadratic Fields * Class Number of Cyclotomic Fields * Miscellaneous Results about the Class Number of Cyclotomic Fields

Additional information

NPB9780387950709
9780387950709
0387950702
Classical Theory of Algebraic Numbers by Paulo Ribenboim
New
Hardback
Springer-Verlag New York Inc.
2001-03-30
682
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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