MM809: Commutative Algebra (5 ECTS)

STADS: 13004101

Level
Master's level course

Teaching period
The course is offered in the autumn semester.
According to needs.

Teacher responsible
Email: ortega@imada.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Ubegrænset deltagerantal. 4. kvartal.

Prerequisites:
None

Academic preconditions:
The student must have basic knowledge of ring theory.

Course introduction
The course introduces the student to some more advanced results in ring and module theory, and provides the first steps in algebraic geometry.

Expected learning outcome
At the end of the course the student will be able to:
- reproduce definitions in the theory of commutative algebra within the scope of the course’s syllabus
- reproduce results, together with their proofs, within the scope of the course’s syllabus
- apply the theory to solve problems in commutative algebra within the scope of the course's syllabus
- relate the results within the scope of the course’s syllabus to each other

Subject overview
Prime and maximal ideals, radical, modules, Nakayama's lemma, projective modules, chain conditions, Artinian and Noetherian rings, local and semilocal rings, module and ring localizations, spectrum of a ring, Hilbert Nullstellensatz, primary decomposition.

Literature
There isn't any litterature for the course at the moment.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Oral examination, grade according to the danish 7-point scale and external censorship.

Reexamination according to the rules approved by the Study Board.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 32 timer
Eksaminatorietimer/opgaveregning: 18 timer
Educational activities

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.