This course will be an introduction to the theory of commutative rings and modules. We will assume familiarity with basic ring theory: notions of prime ideals, modules, localization, noetherian conditions, etc., such as can be found in the first few chapters of Atiyah-Macdonald. After a brief review of these basics, we will develop further properties: Hilbert's nullstellensatz, integral extensions, valuations, dimension theory. We will also discuss regular sequences, depth, and Cohen-Macaulay rings, and we will introduce the notion of a free resolution of a module.
Classes are on Monday, Wednesday, and Friday, 11:30am - 12:25pm, in MW 154.
As a main text, we will use Commutative Ring Theory, by Hideyuki Matsumura. I will occasionally draw on other sources, including the books by Atiyah-Macdonald, Eisenbud, and Bruns-Herzog.
Grades will be based on homework assignments, to be posted here.
| HW1: PDF, due 9/11. |