Math 689: Special Topics in Algebra
Commutative and Homological Algebra
Email: sjw AT math.tamu.edu
This course will cover the basics of commutative and homological
algebra, in preparation for more advanced work in algebra and
related fields. We will plan to work through material from approximately
the first 18 sections of the text Commutative Ring Theory, Matsumura,
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.
Course requirements and grades
Course prerequisite: Math 654 or equivalent.
The course is designed particularly for graduate students in their second
year or beyond, with an interest in algebra, geometry, or topology.
Students who plan to take Math 620 (Algebraic Geometry) in Spring 2016
may benefit by taking this course.
Course grades will be based on homework and class participation.