NMAK14009U Commutative algebra (KomAlg)
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
- 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.
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.
- Category
- Hours
- Exam
- 1
- Exercises
- 21
- Lectures
- 35
- Preparation
- 149
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesThe 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.
Course information
- Language
- English
- Course code
- NMAK14009U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 4
- Schedule
- B (Mon 8-12 + Tues 13-17 + Fri 8-12)
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Jesper Lützen (6-6e77767c6770426f63766a306d7730666d)
Lecturers
Lars Halle