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 - Nakayamas 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