Theory of Algebraic Integers

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.

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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Theory of Algebraic Integers

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