Theory of Algebraic Integers

Richard Dedekind; John Stillwell; John Stillwell

doi:10.1017/CBO9780511623639

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.

"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

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Theory of Algebraic Integers

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Part one - Translator's introduction
pp 1-2

Translator's introduction
pp 3-47

Acknowledgements
pp 47-47

Bibliography
pp 48-50

Part two - Theory of algebraic integers
pp 51-52

Introduction
pp 53-61

1 - Auxiliary theorems from the theory of modules
pp 62-82

2 - Germ of the theory of ideals
pp 83-102

3 - General properties of algebraic integers
pp 103-118

4 - Elements of the theory of ideals
pp 119-152

Index
pp 153-158

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