| # | Lecture |
|---|
| 16 | The spectrum of a ring [pdf] |
| 17 | Krull dimension; Artinian rings |
| 18 | Localisation |
| 19 | Local rings: Nakayama's lemma and Krull's height theorem |
| 20 | Krull's principal ideal theorem |
| 21 | Proof of the height theorem; dimension of polynomial rings |
| 22 | The Cohen–Seidenberg theorems |
| 23 | Valuation rings |
| 24 | Valuations and discrete valuation rings |
| 25 | Artin–Rees, Krull's intersection theorem and the main theorem on DVRs |
| 26 | Dedekind domains |
| 27 | Completion of a discrete valuation ring |
| 28 | p-adic numbers and Hensel's lemma |
| 29 | I-adic completion |
| 30 | What we left out |
