Commutative Algebra, 7.5 credits

Learning outcomes

Knowledge and Understanding
After completed studies the student shall

• be acquainted with the most important concepts and results concerning commutative rings and their modules, and the connection to algebraic geometry and number theory.

Competence and Skills
After completed studies the student shall be able to

• use results about commutative rings in order to solve problems about rings and modules.

Content

Rings, ideals, ring spektrum, modules, Nakayama's lemma. Noetherian rings, Hilbert's basis theorem. Hilbert's Nullstellensatz.

Examinations and grades

Examination, 7.5 credits (Code: A002)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Modes of assessment

• Examination (code A002): Written assignment and oral examination

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Abstract Algebra, 7.5 credits and Linear Algebra II, 7.5 credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course may be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Reid, Miles (1995)
Undergraduate Commutative Algebra
London Mathematical Society, Student Texts 29