Math 689: Introduction to Commutative and Homological Algebra
Prerequisite: Math 654
Course description:
This course will cover the basics of commutative and homological
algebra, in preparation for more advanced work in algebra and
related fields. We will work through material from approximately
the first 18 sections of the text by Matsumura, Commutative Ring
Theory. Specifically, this includes Noetherian rings, primary
decomposition, integral dependence, Nullstellensatz, dimension
theory, chain complexes, resolutions, the Hilbert Syzygy Theorem,
Ext, Tor, and further topics as time permits, such as projective
dimension, depth, and Cohen-Macaulay and Gorenstein rings.
My syllabus from Fall 2015 is at
http://www.math.tamu.edu/~sjw/math689_syllabus.html
and I do not expect to make any major changes to this.