Commutative Algebra

The UMP of the residue class ring.

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


MIT Course Number


As Taught In

Fall 2008



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Course Features

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.

Steven Kleiman. 18.705 Commutative Algebra, Fall 2008. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed). License: Creative Commons BY-NC-SA

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