Faculty of Science

Commutative Algebra (KomAlg)
Provider: Faculty of Science

Activity no.: 5590-23-07-31
	Enrollment deadline: 01/02/2023

Place

Department of Mathematical Sciences

Date and time

06.02.2023, at: 08:00 - 14.04.2023, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Karim Alexander Adiprasito E-mail address: ka@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 3

Scheme group

Exam form

Oral examination, 30 minutes

Exam details

The student will have 30 minutes preparation before the exam.

Exam aids

Only certain aids allowed

Grading scale

Passed / Not passed

Criteria for exam assessment

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

Exam re-examination

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.

Course workload

Course workload category	Hours
Lectures	35.00
Exercises	21.00
Exam	1.00
Preparation	149.00

Sum	206.00

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.

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