NMAK14009U Commutative Algebra (KomAlg)

Volume 2021/2022
Education

MSc Programme in Mathematics

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.

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.

Algebra 2 (Alg2) or similar.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours lectures and 3 hours exercises each week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 149
  • Exercises
  • 21
  • Exam
  • 1
  • Total
  • 206
Written
Oral
Individual
Collective
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.

Credit
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.

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
Re-exam

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 assesment

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