MA8202 - Commutative Algebra
Lessons are not given in the academic year 2018/2019
The course is taught every third year, if there are enough students. Next time spring 2020. If there are few students, there will be guided self-study.
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.
The contents of the course may vary, but it will have a core consisting of the following: Ideals, prime and maximal ideals, Hilberts 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,
The students should be learn the topics mentioned above of and be able to conduct researches in commutative algebra and its applications.
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.
Recommended previous knowledge
MA3201 Rings and modules, MA3202 Galois theory. Having taken MA3204 Homological algebra will be an advantage.
M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra
- * The location (room) for a written examination is published 3 days before examination date.