Commutative Algebra (KomAlg)

Course content

- 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.


MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

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.

5 hours lectures and 3 hours exercises each week for 7 weeks

Algebra 2 (Alg2) or similar.

Academic qualifications equivalent to a BSc degree is recommended.

Feedback by final exam (In addition to the grade)

Written feedback will be given on the mandatory assignment. Oral feedback will be given on students’ presentations in class. Individual feedback will be given via corrections to the mandatory assignment, as well as in connection with the oral exam. Collective feedback will be given through comments by the TA on blackboard presentation by students at the exercise sessions.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
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. The mandatory assignment must be approved no later than three weeks before the beginning of the re-exam week in order to take the re-exam.

Criteria for exam assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

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


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 3
No limit
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Søren Galatius   (8-6c667166796e7a78457266796d33707a336970)
  • Shahar Carmeli   (7-6765767169706d447165786c326f7932686f)


Saved on the 24-08-2023

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