Commutative Algebra (MAGIC073) |
GeneralThis course is part of the MAGIC core. Description
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. SemesterSpring 2019 (Monday, January 21 to Friday, March 29) Hours
Timetable
PrerequisitesN/A
Syllabus1. Rings, Ideals, Homomorphisms
2. Modules 3. Localization 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 Bibliography
Note: Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) AssessmentThe assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be a total 6 of questions. You should attempt and submit your answers to 4 questions of your choice. You will need the equivalent of two questions (answered completely and essentially correctly) to pass.
FilesFiles marked L are intended to be displayed on the main screen during lectures. Recorded LecturesPlease log in to view lecture recordings. |