NMAK14009U Commutative algebra (KomAlg)

Volume 2014/2015
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
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.

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.
5 hours lectures and 3 hours exercises each week for 7 weeks
  • Category
  • Hours
  • Exam
  • 1
  • Exercises
  • 21
  • Lectures
  • 35
  • Preparation
  • 149
  • Total
  • 206
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
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
Exam period
Several internal examiners
Criteria for exam assesment

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