The rings of dimension two

Introduction v

Chapter 0 Preliminaries 1
1. Global dimensions 1
2. Noetherian rings 6
3. Dimension zero 7

Chapter 1 Dimension One 9
1. Tor-dimension one 9
2. Global dimension one 10
3. Finitistic dimension one 13
4. The minimal spectrum 14
5. Generating ideals efficiently 16

Chapter 2 Local Rings (I) 19
1. Classification 19

Chapter 3 Conductors, Cartesian Squares, and Projectivity 25
1. Conductors and the descent of projectivity 25
2. Cartesian squares (I) 28

Chapter 4 Local Rings (II) 31
1. F-rings 31
2. Cardinality conditions 32
3. Fiber products 35
4. Global dimension of F-rings 36

Chapter 5 Change of Rings and Dimensions 41
1. Macaulay extensions 42
2. Finitely generated modules 46
3. Some equalities of dimensions 46
4. Divisibility 48
5. Local rings of Tor-dimension two 54
6. Difficulties in higher dimensions 56

Chapter 6 Finitely Generated Ideals 59
1. Coherence 59
2. Burch's theorem revisited 61
3. The Delta-theorem 63
4. Generating prime ideals efficiently 66
5. Noetherianization 6

Chapter 7 Domains 71
1. x_0-Noetherian domains 71
2. Symmetric algebras  75
3. Sheaf representation 82

Chapter 8 Coherence of Polynomial Rings 85
1. A remark of Gruson's 85
2. Rings of global dimension two 86
3. The lambda-dimension of a ring 89
4. Stability 93

References 97

Index 101