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.
- 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.

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 conducted as flipped classroom, (that is as discussions of the course material. Students are expected to participate in discussions of the course material during the flipped classrooms hours) and 3 hours exercises each week for 7 weeks.

Algebra 2 (Alg2) or similar.

Academic qualifications equivalent to a BSc degree is recommended.

Oral
Individual
Collective
Feedback by final exam (In addition to the grade)

Oral feedback will be given on students’ presentations in class. Individual feedback will be given 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.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral exam without preparation time
Aid
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
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
  • Preparation
  • 149
  • Exercises
  • 21
  • Exam
  • 1
  • English
  • 206