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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.


Autumn 2016 (Monday, October 3 to Friday, December 9)


  • Tue 12:05 - 12:55
  • Fri 11:05 - 11:55




1. 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


Photo of Amos Ajibo
Amos Ajibo
Photo of Mehsin Al-Showali
Mehsin Al-Showali
Photo of Gabriele Bocca
Gabriele Bocca
(East Anglia)
Photo of Francesca Fedele
Francesca Fedele
Photo of Dominic Foord
Dominic Foord
Photo of Christopher Foster
Christopher Foster
Photo of Zoltan Kocsis
Zoltan Kocsis
Photo of Shilan M.Salim
Shilan M.Salim
Photo of James Macpherson
James Macpherson
(East Anglia)
Photo of Entesar Nasr
Entesar Nasr
Photo of Andrea Pachera
Andrea Pachera
Photo of Erik Paemurru
Erik Paemurru
Photo of Francesco Parente
Francesco Parente
(East Anglia)
Photo of Nebojsa Pavic
Nebojsa Pavic
Photo of Edward Pearce
Edward Pearce
Photo of Shi Qiu
Shi Qiu
Photo of Raul Sanchez Galan
Raul Sanchez Galan
Photo of Jack Saunders
Jack Saunders
Photo of Christopher Seaman
Christopher Seaman
Photo of Fabio Tanania
Fabio Tanania
Photo of Motiejus Valiunas
Motiejus Valiunas
Photo of Matty Van Son
Matty Van Son
Photo of George Witty
George Witty
(East Anglia)
Photo of Di Zhang
Di Zhang


Introduction to commutative algebraAtiyah and Macdonald
Steps in commutative algebraSharp
Commutative algebra with a view toward algebraic geometryEisenbud


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.)


The exam will consist of 6 problems taken from the Weekly Problem Sheets. Equivalent of 65 percent is required for a pass mark.

Files:Exam paper
Released: Monday 9 January 2017 (438.5 days ago)
Deadline: Sunday 22 January 2017 (424.5 days ago)

The exam will consist of 6 problems taken from the Weekly Problem Sheets. Equivalent of 65 percent is required for a pass mark.

You can use any books, notes or other sources but you should not discuss the exam with anyone before its submission.

Recorded Lectures

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