Commutative Algebra (KomAlg)
Course 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.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
Competencies:
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 4 hours exercises each week for 7 weeks
Advanced vector spaces (AdVec) and 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.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes (30-minute preparation time)
- 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 during preparation.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
- Re-exam
-
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 assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 35
- Preparation
- 142
- Exercises
- 28
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK14009U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 3
- Schedulegroup
-
C
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Nidhi Kaihnsa (5-746f6a6e6f4673677a6e34717b346a71)
- Alexander F Taveira Blomenhofer (3-657866447165786c326f7932686f)
- Jesper Grodal (2-6d6a437064776b316e7831676e)
Teacher
Postdoc
Er du BA- eller KA-studerende?
Kursusinformation for indskrevne studerende