MATH 6340 - Commutative Algebra with Applications in Algebraic Geometry

Irena Peeva, fall 2015.

Commutative Algebra is the theory of commutative rings and their modules. We will cover several basic topics: localization, primary decomposition, dimension theory, flatness, completion, integral extensions, Hilbert polynomials. The lectures will emphasize connections between Commutative Algebra and Algebraic Geometry.

Prerequisites: A good background in abstract algebra.

Recommended Textbooks:

1. D. Eisenbud, Commutative Algebra.
2. M. Atiyah and I. MacDonald, Introduction to Commutative Algebra.
3. H. Matsumura, Commutative ring theory.