Commutative Algebra
An MIT OpenCourseWare graduate-level course covering the core machinery of commutative algebra. Topics include Noetherian rings and modules, the Hilbert basis theorem, the Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, discrete valuation rings, filtrations, length, Artinian rings, Hilbert polynomials, tensor products, and dimension theory. The course is presented through MIT's OpenCourseWare platform, which provides lecture notes and problem sets used in the actual MIT classroom. Materials are free to access and reuse under a Creative Commons license, though no certificate or instructor interaction is offered. Suited to students who already have a solid grounding in abstract algebra and want to move into the ring- and module-theoretic foundations underlying algebraic geometry and number theory.