Ideal Theory

D. G. Northcott

doi:10.1017/CBO9780511565908

Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected algebraic theory those results which play outstanding roles in the geometric applications.

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Ideal Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Author's Preface
pp vii-viii

Preliminaries
pp 1-3

Chapter I - THE PRIMARY DECOMPOSITION
pp 4-30

Chapter II - RESIDUE RINGS AND RINGS OF QUOTIENTS
pp 31-48

Chapter III - SOME FUNDAMENTAL PROPERTIES OF NOETHERIAN RINGS
pp 49-62

Chapter IV - THE ALGEBRAIC THEORY OF LOCAL RINGS
pp 63-83

Chapter V - THE ANALYTIC THEORY OF LOCAL RINGS
pp 84-100

Notes
pp 101-109

References
pp 110-110

Index of Definitions
pp 111-111

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