MATH 634: Commutative Algebra (spring 2008)
Instructor: Ken Brown
Class will start January 29th.
Tentative list of topics:
- Groebner bases
- Ideals: localization, prime ideals, and operations on ideals
- Modules: graded rings and modules, syzygies, free resolutions
- Noether normalization and Hilbert's nullstellensatz
- integral dependence, going up/down, integral closure
- Primary decomposition in Noetherian rings
- Discrete valutation rings
- Hilbert functions and dimension theory
- Tor and Ext, flatness
- (Time permitting) Cohen-Macaulay rings, depth, regular sequences