Login for PhD students/staff at UCPH      Login for others
Commutative Algebra (KomAlg)
Provider: Faculty of Science

Activity no.: 5590-23-07-31 
Enrollment deadline: 01/02/2023
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time06.02.2023, at: 08:00 - 14.04.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserKarim Alexander Adiprasito    E-mail address: ka@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 3
Scheme groupC
Exam formOral examination, 30 minutes
Exam detailsThe student will have 30 minutes preparation before the exam.
Exam aidsOnly certain aids allowed
Grading scalePassed / Not passed
Criteria for exam assessmentThe student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Exam re-examinationThe 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.
Course workload
Course workload categoryHours
Lectures35.00
Exercises21.00
Exam1.00
Preparation149.00
Sum206.00
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.

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.

Teaching and learning methods
5 hours lectures conducted as flipped classroom, (that is as discussions of the course material. Students are expected to participate in discussions of the course material during the flipped classrooms hours) and 3 hours exercises each week for 7 weeks.

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.