Contents
Preface xiii
Description of the chapters 1
Chapter I. Integral closure 5
1. Introduction 5
2. Integral elements 9
3. Products of ideals 16
4. Noetherian rings 20
5. Rings of dimension 1 28
6. Dedekind domains 31
Chapter II. Plane curves 35
1. Introduction 35
2. Rings of functions 38
3. Points and maximal ideals 45
4. Morphisms of curves 47
5. Singular points 51
6. Localization 57
7. More on dimension 63
8. Local principal ideal domains 67
9. Localization of modules 71
10. Hilbert's Basis Theorem 76
11. More rings of functions 77
Chapter III. Factorization of ideals 85
1. Introduction 85
2. Unique factorization of ideals 88
3. Ramification index and residual degree 93
4. Explicit factorizations 98
5. Ramified and unramified primes 101
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