Course details
A core MAGIC course
Semester
- Autumn 2020
- Monday, October 5th to Friday, December 11th
Hours
- Live lecture hours
- 20
- Recorded lecture hours
- 20
- Total advised study hours
- 80
Timetable
- Mondays
- 12:05 - 12:55 (UK)
- Thursdays
- 13:05 - 13:55 (UK)
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.
Weekly problem sheets and solutions for them are given.
Prerequisites
N/A
Syllabus
1. Rings, Ideals, Homomorphisms
1a. The prime and maximal spectra of a ring.
2. Modules
3. Localization
4. Noetherian rings
5. Primary decomposition
6. Height of ideals
7. Integral extensions
8. Algebraic sets and their dimension
Lecturer
-
PL
Dr Paul Levy
- University
- University of Lancaster
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and 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.
Assessment
The assessment for this course will be released on Monday 11th January 2021 at 00:00 and is due in before Sunday 24th January 2021 at 23:59.
Assessment will be via a single take-home (open book) exam. All questions should be completed. The exam will be released on 11th January, deadline for submission 25th January. The pass mark is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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