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.
Weekly problem sheets and solutions for them are given.
Autumn 2019 (Monday, October 7 to Friday, December 13)
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
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The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be 5 or 6 questions, with a total of 100 marks. You will need a mark of 50 to pass.
No assignments have been set for this course.
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