MAGIC073: Commutative Algebra

Course details

A core MAGIC course


Autumn 2022
Monday, October 3rd to Friday, December 9th


Live lecture hours
Recorded lecture hours
Total advised study hours


We cover the basics of Commutative Algebra, roughly corresponding to the book by Atiyah-MacDonald. Whenever possible we take a geometric perspective on the subject, that is, we 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. 

2. Modules 

3. Localization 

4. Noetherian rings 

5. Primary decomposition 

6. Height of ideals 

7. Integral extensions 

8. Algebraic sets and their dimension 


  • PL

    Dr Paul Levy

    University of Lancaster


No bibliography has been specified for this course.


The assessment for this course will be released on Monday 9th January 2023 and is due in by Saturday 21st January 2023 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


Only consortium members have access to these files.

Please log in to view course materials.


Please log in to view lecture recordings.