Title of the course: On Dedekind domains and their generalizations (Krull domains)
Instructor: Dr. Haleh Hamdi
Institution: Institute for Research in Fundamental Sciences (IPM)
Dates: 11-24 September 2023
Prerequisites: Commutative rings, ideals, modules, Noetherian modules and rings
Level: Graduate, advanced undergraduate.
Abstract:
The purpose of the first week will be to introduce some properties of Dedekind domains and injective modules, and then to examine the behavior of injective modules over Dedekind domains. As a generalization of Dedekind domains, Krull domains play an important role in commutative algebra. In the second week, we will focus on some characterizations of Krull domains. Emphasis will be given to one of the most prominent theorems in commutative algebra, the Mori-Nagata theorem, which states that the integral closure of a Noetherian domain is a Krull domain. The concepts taught in the first week will not be prerequisites for the second week.
Language: English
Textbooks:
1. Fossum, R.M. 1973. The divisor class group of a Krull domain. New York: Springer.
2. Gilmer, R. 1972.  Multiplicative ideal theory. New York: Marcel Dekker.
3. Rotman, J. 1979. An Introduction to Homological Algebra. New York: Academic Press.