Classical Theory of Algebraic Numbers

Paulo Ribenboim

ISBN 10: 1441928707 / ISBN 13: 9781441928702

Published by Springer New York, 2010

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The exposition of the classical theory of algebraic numbers is clear and thorough, and there is&nbspa large number of exercises as well as worked out numerical examples.&nbspA careful study of this book will provide a solid background to the learning o.

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Bibliographic Details

• Title: Classical Theory of Algebraic Numbers
• Publisher: Springer New York
• Publication Date: 2010
• Language: English
• ISBN 10: 1441928707
• ISBN 13: 9781441928702
• Binding: Soft cover
• Edition: 2nd Edition
• Condition: New

About this title

Synopsis

After a brief introduction reviewing the concepts of principal ideal domains and commutative fields, the book discusses residue classes (for example, the integers mog=dulo some number m); quadratic residues; algebraic integers (that is, objects that behave like integers in arbitrary algebraic structures), their discriminant; decomposition, norm, and classes of ideals; the ramification index; and the fundamental theorem of Abelian extensions. The theorems and definitions are carefully motivated, and the author frequently stops to explain how things fit together and what will come next. There are a great many exercises and many useful examples at a

Review

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." (Gábor 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)