Commutative Algebra

J. T. Knight

doi:10.1017/CBO9780511661822

This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.

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Commutative Algebra

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

1 - Preliminaries
pp 1-15

2 - Flatness
pp 16-31

3 - Fractions
pp 32-60

4 - Supporting and associated prime ideals
pp 61-71

5 - Integers
pp 72-84

6 - Some geometrical results
pp 85-88

7 - Valuation rings
pp 89-104

8 - Prüfer and Dedekind rings
pp 105-112

9 - General Exercises
pp 113-115

Appendix 1 - Categories
pp 116-120

Appendix 2 - The constructible topology
pp 121-123

Bibliography
pp 124-124

Indices
pp 125-128

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Commutative Algebra

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