Mathematics 221

Commutative Algebra (123232)

Mihnea Popa

2025 Fall (4 Credits)

Schedule: MW 1200 PM - 0115 PM

Instructor Permissions: None

Enrollment Cap: n/a

Commutative Algebra lies at the foundations of Number Theory and Algebraic Geometry. It plays an important role in Algebraic Topology, Geometry and other fields. We will cover the main topics of Commutative Algebra and give a taste of its applications. Starting from generalities on rings, modules and ideals, localization and primary decomposition in Noetherian rings and modules, we then move to integral extensions, going-up and going-down, Noether normalization and Hilbert’s Nullstellensatz, dimension theory. The final part of the class will cover graded rings, Hilbert polynomials and homological methods (if time permits, including regular local rings).

Recommended Prep:

Mathematics 122, 123.

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