MAGIC073: Commutative Algebra

Course details

A core MAGIC course


Autumn 2023
Monday, October 2nd to Friday, December 8th


Live lecture hours
Recorded lecture hours
Total advised study hours


13:05 - 13:55 (UK)
11:05 - 11:55 (UK)

Course forum

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The first two sections review some fundamental concepts of commutative algebra, while the remaining sections present topics which may not have been seen in an undergraduate introductory course on commutative algebra.
The content of the notes, which has been selected from the material in the references at the end, is intended to prepare the learner to explore the applications of commutative algebra to a broad range of research areas.

Within the lecture notes, there are several exercises at the end of each section.
Every student is encouraged to attempt as many of these as they wish, and more from the selected bibliography.
Your lecturer will recommend some (bi-)weekly exercises, taken from the notes, and the solutions of these will be made available on the MAGIC website by the end of the course.
Every student should be familiar with the relevance of engaging with the practical aspects of a course.

The entire material covered in lectures is examinable, including the exercises. More details about examination will follow in due time.

For the computer-algebra enthusiasts, I included the reference of a resource which may be of interest, and I also would recommend the numerous possibilities offered by MAGMA:
We do not use any of them in the course, and no assessment component will require any knowledge of software.

Accessibility: please contact your lecturer if you need an alternative format for the lecture notes and exercises.


No prerequisites are absolutely essential, but it helps to have some background in commutative rings and ideal theory.


1. Commutative algebra: the essentials (rings, ideals, homomorphisms, localisation)
2. Modules
3. Integral dependence
4. Prime and maximal ideal spectra
5. A brief taste of algebraic geometry: algebraic sets and Hilbert's Nullstellensatz
6. Primary decomposition
7. Dimension in commutative rings.


  • Professor Nadia Mazza

    Professor Nadia Mazza

    University of Lancaster


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.

  • A Primer of Commutative Algebra (J. Milne, web) Download
  • A Singular introduction to commutative algebra (G.-M. Greuel and G. Pfister, book)
  • Alg\`ebre commutative. \'Elements de math\'ematiques [French], or English translation; any edition (N. Bourbaki, book)
  • Algebra (T. W. Hungerford, book)
  • Algebra (S. Lang, book)
  • Algebra - A graduate course (I.M. Isaacs, book)
  • Basic Algebra I and II (N. Jacobson, book)
  • Commutative algebra: Constructive methods. Finite projective modules (H. Lombardi and C. Quitt'e, book)
  • Commutative algebra. With a view toward algebraic geometry (D. Eisenbud, book)
  • Introduction to Commutative Algebra (M. Atiyah and I. MacDonald, book)
  • Undergraduate commutative algebra (M. Reid, book)


The assessment for this course will be released on Monday 8th January 2024 at 00:00 and is due in before Monday 22nd January 2024 at 11:00.

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.


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