18.705 Commutative Algebra

Fall 2008

The UMP of the residue class ring.
The universal mapping property (UMP) of the residue class ring. (Image by MIT OpenCourseWare.)

Course Description

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.
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Staff

Instructor:
Prof. Steven Kleiman

Course Meeting Times

Lectures:
2 sessions / week
1.5 hours / session

Level

Graduate