Commutative algebra - Department of Mathematical Sciences - old ...

6 CONTENTS
5.3. Localization of modules 68
5.4. Exactness and localization 70
5.5. Flat ring homomorphisms 71
6. Finite modules 73
6.1. Finite Modules 73
6.2. Free Modules 75
6.3. Cayley-Hamilton’s theorem 77
6.4. Nakayama’s Lemma 78
6.5. Finite Presented Modules 80
6.6. Finite ring homomorphisms 83
7. Modules of finite length 85
7.1. Simple Modules 85
7.2. The Length 85
7.3. Artinian Rings 87
7.4. Localization 90
7.5. Local artinian ring 91
8. Noetherian modules 93
8.1. Modules and submodules 93
8.2. Noetherian rings 94
8.3. Finite type rings 95
8.4. Power series rings 97
8.5. Fractions and localization 98
8.6. Prime filtrations of modules 98
9. Primary decomposition 101
9.1. Support of modules 101
9.2. Ass of modules 103
9.3. Primary modules 106
9.4. Decomposition of modules 106
9.5. Decomposition of ideals 108
10. Dedekind rings 111
10.1. Principal ideal domains 111
10.2. Discrete valuation rings 112
10.3. Dedekind domains 113
Bibliography 117
Index 119