1 | Rings and Modules | 3 |
---|---|---|
1.1 Ideals and Radicals | 3 | |
1.2 Polynomial rings and Localization of rings | 8 | |
1.3 Modules | 11 | |
1.4 Zariski Tolpology | 12 | |
Exercises | 14 | |
2 | Noetherian Rings | 17 |
2.1 Noetherian Rings and Modules | 17 | |
2.2 Primary Decomposition of Ideals | 19 | |
2.3 Artinian Rings and Modules | 23 | |
2.4 Krull's Principal Ideal Theorem | 27 | |
Exercises | 14 | |
3 | Integral Extensions | 32 |
3.1 Integral Extensions | 32 | |
3.2 Noether Normalization | 35 | |
3.3 Finiteness of Integral Closure | 38 | |
Exercises | 42 | |
4 | Dedekind Domains | 44 |
4.1 Dedekind Domains | 45 | |
4.2 Extensions of Primes | 50 | |
Exercises | 42 | |
A | Appendix: Primary Decomposition of Modules | 55 |
A.1 Associated Primes of Modules | 55 | |
A.2 Primary Decomposition of Modules | 58 | |
Exercises | 62 | |
References | 63 | |
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