MAU34102 Commutative algebra
| Module Code | MAU34102 |
|---|---|
| Module Title | Commutative algebra |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Sergey Mozgovoy |
| Module Prerequisites | MAU22102 Fields, rings and modules |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 15% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Module Content
- Exact sequences and tensor products of modules.
- Rings of fractions.
- Noetherian and Artinian rings, Hilbert's basis theorem, primary decomposition.
- Integral dependence, Noether's normalization theorem, Hilbert's Nullstellensatz.
- Discrete valuation rings, Dedekind domains, p-adic numbers, Hensel's lemma.
- Dimension theory.
Recommended Reading
- Introduction to commutative algebra by Atiyah and MacDonald.
- Commutative algebra, volumes I and II, by Zariski and Samuel.
- Commutative algebra by Eisenbud.