Schedule, syllabus and examination date

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Course content

This course gives an introduction to commutative rings and their modules. We study concepts such as localization, decomposition of modules, chain conditions for rings and modules, and dimension theory. The course gives a relevant background for studies in algebraic geometry, but also relates the theory to problems in number theory.

Learning outcome

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 the concept of direct limit and you can compute this limit in some non-trivial examples;
  • know how to define tensor products of modules and are familiar with the concept of flatness;
  • know Krull-Cohen-Seidenberg theory;
  • know the basic results in the dimension theory for local rings;
  • know how to complete a ring in an ideal.

Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

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

Prerequisites

Recommended previous knowledge

Overlapping courses

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours of lectures/exercises per week.

Examination

1 mandatory assignment.

Final written examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

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.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

Master

Teaching

Every autumn

Examination

Every autumn

Teaching language

English

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