| Week Starting | Topics |
|---|---|
| 18 Aug | Rings, homomorphisms, ideals |
| 25 Aug | Prime and maximal ideals, fields, integral domains PIDs and UFDs, local rings |
| 1 Sep | Operations on ideals, coprime ideals, the Chinese remainder theorem |
| 8 Sep | Modules, Nakayama's lemma |
| 15 Sep | Exact sequences, additive functions, the tensor product |
| 22 Sep | Exactness of the tensor product, flat modules, algebras |
| 29 Sep | Rings of fractions, modules of fractions |
| 6 Oct | Local properties, prime ideals in fraction rings |
| 13 Oct | Integral dependence, lying over and going up |
| 20 Oct | Chain conditions, simple modules and composition series |
| 27 Oct | Noetherian rings, Noether normalisation |
| 3 Nov | Hilbert's nullstellensatz, Hilbert's basis theorem |
| 10 Nov | Artinian rings |
| 17 Nov | DVRs |
| 24 Nov | Revision |
Course progression
Published Aug. 29, 2025 4:34 PM
- Last modified Aug. 29, 2025 4:34 PM