# InfoCoBuild

## Introduction to Commutative Algebra

Introduction to Commutative Algebra. Instructor: Prof. A. V. Jayanthan, Department of Mathematics, IIT Madras. This is an introductory course in Commutative Algebra where most basic tools on commutative rings and modules over commutative rings are developed. This course is essential for anyone who wants to do research in areas such as commutative algebra, algebraic geometry, algebraic number theory etc. (from nptel.ac.in)

 Lecture 32 - Primary Decomposition (cont.)

Go to the Course Home or watch other lectures:

 Ring Theory Basics Lecture 01 - Review of Ring Theory Lecture 02 - Review of Ring Theory (cont.) Lecture 03 - Ideals in Commutative Rings Ideals Lecture 04 - Operations on Ideals Lecture 05 - Properties of Prime Ideals Lecture 06 - Colon and Radical of Ideals Module Theory Basics Lecture 07 - Radicals, Extension and Contraction of Ideals Lecture 08 - Modules and Homomorphisms Lecture 09 - Isomorphism Theorems and Operations on Modules Homomorphism and Nakayama's Lemma Lecture 10 - Operations on Modules (cont.) Lecture 11 - Module Homomorphism and Determinant Trick Lecture 12 - Nakayama's Lemma and Exact Sequences Properties of Modules Lecture 13 - Exact Sequences (cont.) Lecture 14 - Homomorphisms and Tensor Products Lecture 15 - Properties of Tensor Products Localization Lecture 16 - Properties of Tensor Products (cont.) Lecture 17 - Tensor Product of Algebras Lecture 18 - Localization Lecture 19 - Localization (cont.) Localization and Integral Dependence Lecture 20 - Local Properties Lecture 21 - Further Properties of Localization Lecture 22 - Integral Dependence Going-up Theorem Lecture 23 - Integral Extensions Lecture 24 - Lying Over and Going-up Theorems Lecture 25 - Going-down Theorem Going-down Theorem and Chain Conditions Lecture 26 - Going-down Theorem (cont.) Lecture 27 - Chain Conditions Lecture 28 - Noetherian and Artinian Modules Lecture 29 - Properties of Noetherian and Artinian Modules, Composition Series Properties of Noetherian Rings Lecture 30 - Further Properties of Noetherian and Artinian Modules and Rings Lecture 31 - Hilbert Basis Theorem and Primary Decomposition Lecture 32 - Primary Decomposition (cont.) Primary Decomposition and Artinian Rings Lecture 33 - Uniqueness of Primary Decomposition Lecture 34 - 2nd Uniqueness Theorem, Artinian Rings Lecture 35 - Properties of Artinian Rings Noether Normalization and Hilbert's Nullstellensatz Lecture 36 - Structure Theorem of Artinian Rings Lecture 37 - Noether Normalization Lecture 38 - Hilbert's Nullstellensatz