Course details
Semester
 Autumn 2024
 Monday, October 7th to Friday, December 13th
Hours
 Live lecture hours
 20
 Recorded lecture hours
 0
 Total advised study hours
 80
Timetable
 Mondays
 13:05  13:55 (UK)
 Tuesdays
 10:05  10:55 (UK)
Course forum
Visit the https://mathsmagic.ac.uk/forums/magic073commutativealgebra
Description
In this course, the first two sections present the essential 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 has been selected from the material in the references at the end, and students are encouraged to consult these textbooks if they want to explore some topics in greater depth, or their applications to a broad range of research areas.
Within the lecture notes, there are several exercises at the end of each section. The lecture notes are a "living document"", which may be altered during the semester to reflect the lectures, and possibly respond to student feedback (always welcome).
Every student is encouraged to attempt as many exercises as they can, including from the selected bibliography.
Your lecturer will recommend some exercises, mostly taken from the notes. Model solutions of these will be made available on the MAGIC website by the end of the course.
Every student is assumed to understand the importance of engaging with the practical aspects of a course.
The entire material covered during the lectures (not necessarily all the lecture notes) is examinable, including the exercises. More details about examination will follow in due time.
For the computeralgebra enthusiasts, I included a reference of a resource which may be of interest, and I also would recommend the numerous possibilities offered by MAGMA: http://magma.maths.usyd.edu.au/magma/ and other software such as python or sagemath.
No assessment will require the use of such software, but, unless specified, it's not forbidden to use computing tools.
Accessibility: please contact your lecturer if you need an alternative format for the lecture notes and exercises.
Prerequisites
Syllabus
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.
Lecturer

Professor Nadia Mazza
 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.
 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)
Assessment
The assessment for this course will be released on Monday 13th January 2025 at 00:00 and is due in before Friday 24th January 2025 at 11:00.
Assessment for all MAGIC courses is via takehome 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 uptodate with the course, the expectation is it should take at most 3 hoursâ€™ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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