18.705 | Fall 2008 | Graduate
Commutative Algebra
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. …
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.
Course Info
Learning Resource Types
assignment Problem Sets
The UMP of the residue class ring.
The universal mapping property (UMP) of the residue class ring. (Image by MIT OpenCourseWare.)