Commutative Algebra (MAGIC073)
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This course is part of the MAGIC core.
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. Our final destination is the following deep theorem by Auslander-Buchsbaum-Serre: a local commutative ring R is regular if and only if it has finite global dimension.
Weekly problem sheets and solutions for them are given. Results of the problems marked with a "dagger" sign will be relied on in the lectures.
Spring 2019 (Monday, January 21 to Friday, March 29)
1. Rings, Ideals, Homomorphisms
4. Noetherian rings
5. Primary decomposition
6. Height of ideals
7. Integral extensions
8. Algebraic sets and their dimension
9. A taste of homological algebra
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