Commutative algebra (KomAlg)

Course content

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

Education

MSc Programme in Mathematics

Learning outcome

Knowledge:

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.

Skills:

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.

Competences:

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.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
The student will have 30 minutes preparation before the exam.
Aid
All 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
Criteria for exam assessment

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

Single subject courses (day)

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