Commutative Algebra (KomAlg)
- Rings, ideals and modules.
- Homomorphisms, tensor product, flatness, fractions and localization.
- Chain conditions, Noetherian and Artinian rings. Hilbert basis
- 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.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
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.
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 and 3 hours exercises each week for 7 weeks
Algebra 2 (Alg2) or similar.
Academic qualifications equivalent to a BSc degree is recommended.
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.
- 7,5 ECTS
- Type of assessment
Oral examination, 30 minutes
- Type of assessment details
- The student will have 30 minutes preparation before the exam.
- 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 should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 3
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Søren Galatius (8-6a646f64776c7876437064776b316e7831676e)
Are you BA- or KA-student?
Courseinformation of students