NMAK14009U  Commutative Algebra (KomAlg)

Volume 2018/2019

MSc Programme in Mathematics


- Rings, ideals and modules.
- Homomorphisms, tensor product, flatness, fractions and localization.
- Chain conditions, Noetherian and Artinian rings. Hilbert basis
- The Cayley-Hamilton theorem and Nakayama's lemma.
- Integral dependence, normalization. The going up theorem.
- Primary decomposition.
- Connections to geometry. Dimension theory, Hilbert's Nullstellensatz.

Learning Outcome


At the end of the course, the student should:
- Be familiar with the basic notions of commutative algebra.
- Display knowledge and understanding of the course
topics and content at a level suitable for further studies in
commutative algebra and algebraic geometry.


At the end of the course the student is expected to be able
to follow and reproduce arguments at a high abstract level
corresponding to the contents of the course.


At the end of the course the student is expected to be
able to apply basic techniques and results to concrete examples.

Algebra 2 (Alg2) or similar.
5 hours lectures and 3 hours exercises each week for 7 weeks
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
The student will have 30 minutes preparation before the exam.
Exam registration requirements

To be eligible to take the exam the student must have handed in the mandatory homework assignment, and this must have been approved.

Only certain aids allowed

All aids allowed for the preparation. For the oral exam, the student may bring 1 A4 sheet of notes.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

The same as the ordinary exam.
To be eligible to take the re-exam, students who have not already had the mandatory assignment approved must re-submit the assignment no later than two weeks before the beginning of the re-exam week. The mandatory assignment must be approved in order to take the re-exam.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

  • Category
  • Hours
  • Lectures
  • 35
  • Exercises
  • 21
  • Exam
  • 1
  • Preparation
  • 149
  • Total
  • 206