Theory of Algebraic Integers

Theory of Algebraic Integers

by Richard Dedekind
     
 

ISBN-10: 0521565189

ISBN-13: 9780521565189

Pub. Date: 01/28/2004

Publisher: Cambridge University Press

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877. This book is a translation of that work by John Stillwell, who adds…  See more details below

Overview

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877. This book is a translation of that work by John Stillwell, who adds a detailed introduction giving historical background and who outlines the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir offers a candid account of the development of an elegant theory and provides blow by blow comments regarding the many difficulties encountered en route. This book is a must for all number theorists.

Product Details

ISBN-13:
9780521565189
Publisher:
Cambridge University Press
Publication date:
01/28/2004
Series:
Cambridge Mathematical Library Series
Pages:
168
Product dimensions:
5.98(w) x 8.98(h) x 0.39(d)

Table of Contents

Part I. Translator's Introduction: 1. General remarks; 2. Squares; 3. Quadratic forms; 4. Quadratic integers; 5. Roots of unity; 6. Algebraic integers; 7. The reception of ideal theory; Part II. Theory of Algebraic Integers: 8. Auxiliary theorems from the theory of modules; 9. Germ of the theory of ideals; 10. General properties of algebraic integers; 11. Elements of the theory of ideals.

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