- Course Description: In this course, students will learn about Rings and Ideals, Modules, Rings and Modules of Fractions, Hilbert Basis Theorem, Cayley-Hamilton Theorem, Noether Normalization, the Nullstellensatz, Localization, Local and Global Fields, Local Zeta Functions, Primary Decomposition, Integral Dependence and Valuations, Chain Conditions, Noetherian Rings, Artin Rings, Discrete Valuation Rings and Dedekind Domains, Filtrations, Completions, Hilbert Polynomials, and Dimension Theory.
- SIS Description: The foundations of commutative algebra, algebraic number theory, or algebraic geometry.
1. Introduction to Commutative Algebra, by Michael Atiyah and Ian Macdonald
2. Commutative Algebra Notes, by Craig Huneke
3. Commutative Algebra, by Hideyuki Matsumura
4. The Stacks Project, by Aise Johan de Jong
5. Algebraic Geometry, by Robin Hartshorne
6. Algebraic Number Theory, by Jürgen Neukirch