MAT4200 – Commutative Algebra

After completing the course you

• know the definition of commutative rings, local rings, prime and maximal ideals, and modules over commutative rings
• are familiar with the notions of noetherian and artinian rings and modules
• know how to localize rings and modules, and are familiar with important applications of localization
• know the Hilbert basis theorem and the Hilbert Nullstellensatz
• are familiar with the concepts of support and associated primes
• know the definition of an exact sequence of modules, and you also know important properties and applications of exact sequences
• know how to define tensor products of modules and are familiar with the concept of flatness
• know the "Going-Up"-theorem of Cohen-Seidenberg
• know the basic results in the dimension theory for local rings

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

• MAT2200 – Groups, Rings and Fields

4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Final written exam or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.

This course has 1mandatory assignment that must be approved before you can sit the final exam.

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.