The Theory of Algebraic Numbers

Harry Pollard; Harold Diamond

doi:10.5948/9781614440093

The MAA is pleased to re-issue the early Carus Mathematical Monographs in ebook and print-on-demand formats. Readers with an interest in the history of the undergraduate curriculum or the history of a particular field will be rewarded by study of these very clear and approachable little volumes. This monograph makes available in English the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.

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The Theory of Algebraic Numbers

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Contents

Frontmatter
pp i-vi

Dedication
pp vii-vii

Contents
pp viii-x

Preface to First Edition
pp xi-xii

CHAPTER I - Divisibility
pp 1-13

CHAPTER II - The Gaussian Primes
pp 14-24

CHAPTER III - Polynomials over a field
pp 25-43

CHAPTER IV - Algebraic Number Fields
pp 44-58

CHAPTER V - Bases
pp 59-73

CHAPTER VI - Algebraic Integers and Integral Bases
pp 74-87

CHAPTER VII - Arithmetic in Algebraic Number Fields
pp 88-101

CHAPTER VIII - The Fundamental Theorem of Ideal Theory
pp 102-119

CHAPTER IX - Consequences of the Fundamental Theorem
pp 120-138

CHAPTER X - Ideal Classes and Class Numbers
pp 139-145

CHAPTER XI - The Fermat Conjecture
pp 146-159

References
pp 159-159

List of Symbols
pp 160-160

Index
pp 161-162

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