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Commutative Algebra
MATH 221

Course Information

Description

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).

School Faculty of Arts & Sciences
Credits 4
Cross Reg

Available for Harvard Cross Registration

Department Mathematics
Course Component Lecture
Grading Basis FAS Letter Graded
Exam/Final Deadline Dec. 15, 2026
General Education N/A
Quantitative Reasoning with Data N/A
Divisional Distribution Science & Engineering & Applied Science
Course Level Primarily for Graduate Students