Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Commutative algebra (KomAlg)

Practical information
Study year 2016/2017
Time
Block 3
Programme level Full Degree Master
ECTS 7,5 ECTS
Course responsible
  • Lars Halvard Halle (8-706576776c6c6570447165786c326f7932686f)
  • Department of Mathematical Sciences
Course number: NMAK14009U

Course 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.

Recommended prerequisites

Algebra 2 (Alg2) or similar.

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Education

MSc Programme in Mathematics

Studyboard

Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

C
---- SKEMA LINK ----

Teaching and learning methods

5 hours lectures and 3 hours exercises each week for 7 weeks

Capacity

No limit

Language

English

Workload

Category Hours
Lectures 35
Exercises 21
Exam 1
Preparation 149
English 206

Exam

Type of assessment

Oral examination, 30 minutes
The student will have 30 minutes preparation before the exam.

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

Criteria for exam assessment

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

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 mandatory assignment approved must re-submit the assignment no later than 2 weeks before the beginning of the re-exam week. The mandatory assignment must be approved in order to take the re-exam.

Mere information om kurset
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