course-details-portlet

MA8202 - Commutative Algebra

About

Lessons are not given in the academic year 2024/2025

Course content

The contents of the course may vary, but it will have a kernel consisting of ideals, modules, chain conditions, the spectrum of a ring, Hilberts Nullestellensatz, associated primes and decomposition theorems, integral elements and rings, valuation rings, Dedekind rings, graded rings, dimension theory. It can also include regular sequences, Koszul complex, and finally regular, Cohen-Macaulay and Gorenstein rings.

Learning outcome

1. Knowledge. The contents of the course may vary, but it will have a core consisting of the following: Ideals, prime and maximal ideals, Hilbert's Nullstellensatz, modules, operations on modules, localizations with respect to multiplicatively closed sets and with respect to prime ideals, local rings and local properties, localization of modules, chain conditions, noetherian and artinian rings, dimension theory. It may moreover include Dedekind domains, discrete valuation rings, completions, regular sequences, Koszul complexes, Cohen-Macaulay rings, Gorenstein rings.

2. Skills. The students should learn the topics mentioned above and be able to conduct researches in commutative algebra and its applications.

3. Competence. The students should be able to participate in scientific discussions and begin with own reseach in commutative algebra.

Learning methods and activities

Lectures, possibly as a guided self-study.

The course is taught every third year, if there are enough students. Next time spring 2026. If there are few students, there will be guided self-study.

Further on evaluation

Oral exam.

Course materials

M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, together with lecture notes.

More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level

Coursework

No

Language of instruction: English

Location: Trondheim

Subject area(s)
  • Algebra
Contact information

Department with academic responsibility
Department of Mathematical Sciences

Examination

  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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