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

Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral exam without preparation time
Exam registration requirements

To be eligible to take the exam the student must either

1) Have handed in the written homework assignments, and this must have been approved or 

2) have their in-class participation 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 written assignments or their in-class participation approved must (re)submit the assignments. The written assignments 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.