Theory of Algebraic Integers

A translation of a classic work by one of the truly great figures of mathematics.

Richard Dedekind (Author), John Stillwell (Translated by), John Stillwell (Introduction by)

9780521565189, Cambridge University Press

Paperback, published 28 September 1996

168 pages
22.8 x 15.2 x 1.1 cm, 0.236 kg

"The book has historical interest in providing a very clear glimpse of the origins of modern algebra and algebraic number theory, but it also has considerable mathematical interest. It is truly astonishing that a text written one hundred and twenty years ago, well before modern algebraic terminology and concepts were introduced and accepted, can provide a plausible introduction to algebraic number theory for a student today." Mathematical Reviews Clippings 98h

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 instalments in the 'Bulletin des sciences mathematiques' in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir gives a candid account of his development of an elegant theory as well as providing blow-by-blow comments as he wrestled with the many difficulties encountered en route. 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.

Subject Areas: Number theory [PBH]