M/W/F 10-10:50 - Addams Hall 307
Office Hours W 1-3 - SEO 416
References: Introduction to Commutative Algebra (Atiyah--MacDonald), Commutative Algebra with a view towards Algebraic Geometry (Eisenbud), A Primer of Commutative Algebra (Milne), Local Algebra (Serre)
Here's a rough list of topics I plan to cover:
Basics of rings and modules
Noetherianity and Nakayama's Lemma
Localization of rings and modules
Primary decompositions and associated primes
Filtrations, completion, and the associated graded
Integral and finite extensions
Dimension theory
Systems of parameters and the Principle Ideal Theorem
Regular sequences and the Koszul complex
Free and projective resolutions
Homological algebra of regular local rings
Homework 1 (Due 9/17)