Media Storage Type : DVD-ROM
NPTEL Course Name : Advanced Abstract Algebra
NPTEL Subject Matter Expert : Dr. R. K. Sharma
NPTEL Co-ordinating Institute : IIT Delhi
NPTEL Lecture Count : 23
Lecture Titles:
Lecture 1 - Modules
Lecture 2 - Submodules and Direct Sum
Lecture 3 - R-Homomorphism
Lecture 4 - Simple Modules / Semisimple Modules
Lecture 5 - Free Modules: Introduction
Lecture 6 - Free Modules: Results
Lecture 7 - Free Modules
Lecture 8 - Artinian Modules
Lecture 9 - Noetherian Modules
Lecture 10 - Artinian and Noetherian Rings
Lecture 11 - Hilbert Basis Theorem
Lecture 12 - Wedderburn-Artin Theorem
Lecture 13 - Uniform Modules, Primary Modules
Lecture 14 - Smith Normal form over a PID and rank
Lecture 15 - Smith Normal Form
Lecture 16 - Proof of Smith Normal Form
Lecture 17 - Uniqueness of Smith Normal Form
Lecture 18 - Modules over PID
Lecture 19 - Finitely generated modules over PID (Elementary divisor form; Uniqueness)
Lecture 20 - Rational Canonical Form
Lecture 21 - Generalized Jordan form over any field
Lecture 22 - Rings
Lecture 23 - Morphisms and anti-morphisms of rings