NOC:Introduction to Commutative Algebra


Lecture 1 - Review of Ring Theory


Lecture 2 - Review of Ring Theory (Continued...)


Lecture 3 - Ideals in commutative rings


Lecture 4 - Operations on ideals


Lecture 5 - Properties of prime ideals


Lecture 6 - Colon and Radical of ideals


Lecture 7 - Radicals, extension and contraction of ideals


Lecture 8 - Modules and homomorphisms


Lecture 9 - Isomorphism theorems and Operations on modules


Lecture 10 - Operations on modules (Continued...)


Lecture 11 - Module homomorphism and determinant trick


Lecture 12 - Nakayama’s lemma and exact sequences


Lecture 13 - Exact sequences (Continued...)


Lecture 14 - Homomorphisms and Tensor products


Lecture 15 - Properties of tensor products


Lecture 16 - Properties of tensor products (Continued...)


Lecture 17 - Tensor product of Algebras


Lecture 18 - Localization


Lecture 19 - Localization (Continued...)


Lecture 20 - Local properties


Lecture 21 - Further properties of localization


Lecture 22 - Intergral dependence


Lecture 23 - Integral extensions


Lecture 24 - Lying over and Going-up theorems


Lecture 25 - Going-down theorem


Lecture 26 - Going-down theorem (Continued...)


Lecture 27 - Chain conditions


Lecture 28 - Noetherian and Artinian modules


Lecture 29 - Properties of Noetherian and Artinian modules, Composition Series


Lecture 30 - Further properties of Noetherian and Artinian modules and rings


Lecture 31 - Hilbert basis theorem and Primary decomposition


Lecture 32 - Primary decomposition (Continued...)


Lecture 33 - Uniqueness of primary decomposition


Lecture 34 - 2nd Uniqueness theorem, Artinian rings


Lecture 35 - Properties of Artinian rings


Lecture 36 - Structure Theorem of Artinian rings


Lecture 37 - Noether Normalization


Lecture 38 - Hilberts Nullstellensatz