Overview

Full Product Details

Author:   Paulo Ribenboim
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 2001
Dimensions:   Width: 15.60cm , Height: 3.80cm , Length: 23.40cm
Weight:   2.590kg
ISBN:  

9780387950709

ISBN 10:   0387950702
Pages:   682
Publication Date:   30 March 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

Unique Factorization Domains, Ideals, and Principal Ideal Domains.- Commutative Fields.- One.- Residue Classes.- Quadratic Residues.- Two.- 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.- The Fundamental Theorem of Abelian Extensions.- Complements and Miscellaneous Numerical Examples.- Three.- Local Methods for Cyclotomic Fields.- Bernoulli Numbers.- Fermat’s Last Theorem for Regular Prime Exponents.- More on Cyclotomic Extensions.- Four.- 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 Numbers of Quadratic Fields.- Class Number of Cyclotomic Fields.- Miscellaneous Results About the Class Number of Quadratic Fields.- Miscellaneous Results About the Class Number of Cyclotomic Fields.

Reviews

From the reviews of the second edition: <p> This book is a thorough self-contained introduction to algebraic number theory. a ] 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 a ] . The book contains a great amount of material, more than enough for a year-long course. (GAbor Megyesi, Acta Scientiarum Mathematicarum, Vol. 69, 2003) <p> There is a wealth of material in this book. The approach is very classical and global. a ] 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) <p> Ribenboimsa (TM)s a ~Classical Theory of Algebraic Numbersa (TM) is an introduction to algebraic number theory on an elementary level a ] . Ribenboima (TM)s book is a well written introduction to classical algebraic number theory a ] and the perfect textbook for students who need lots of examples. (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1082, 2006)

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)

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