Contents
Preface xi
Chapter 1. The Krull-Remak-Schmidt Theorem 1
§1. KRS in an additive category 1
§2. KRS over Henselian rings 6
§3. R-modules vs. R-modules 7
§4. Exercises 9
Chapter 2. Semigroups of Modules 13
§1. Krull monoids 14
§2. Realization in dimension one 17
§3. Realization in dimension two 23
§4. Flat local homomorphisms 26
§5. Exercises 27
Chapter 3. Dimension Zero 29
§1. Artinian rings with finite Cohen-Macaulay type 29
§2. Artinian pairs 32
§3. Exercises 39
Chapter 4. Dimension One 41
§1. Necessity of the Drozd-Ro˘ ıter conditions 42
§2. Sufficiency of the Drozd-Ro˘ ıter conditions 45
§3. ADE singularities 50
§4. The analytically ramified case 52
§5. Multiplicity two 54
§6. Ranks of indecomposable MCM modules 56
§7. Why MCM modules? 57
§8. Exercises 58
Chapter 5. Invariant Theory 61
§1. The skew group ring 61
§2. The endomorphism algebra 65
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