We cover the basics of Commutative Algebra, roughly corresponding to the book by Atiyah-MacDonald. Whenever possible we take geometric perspective on the subject, that is translate back and forth between algebraic concepts and their geometric counterparts.
No prior knowledge of Commutative Algebra is required as the module starts with basic definitions: rings, ideals, modules and so on. However we take a fast paced approach and go quickly from definitions to nontrivial constructions and theorems sometimes leaving out minor details for the students to work out.
Weekly problem sheets and solutions for them are given.
1. Rings, Ideals, Homomorphisms
1a. The prime and maximal spectra of a ring.
4. Noetherian rings
5. Primary decomposition
6. Height of ideals
7. Integral extensions
8. Algebraic sets and their dimension