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Mathematics
Advanced Abstract Algebra (Web)
Syllabus
Co-ordinated by :
IIT Delhi
Available from :
2012-06-25
Lec :
1
Modules / Lectures
Module 1
Rings
Morphisms and anti-morphisms of rings
Module 2
Modules
Submodules and Direct Sum
R-Homomorphism
Simple Modules/ Semisimple Modules
Free Modules: Introduction
Free Modules: Results
Free Modules
Module 3
Artinian Modules
Noetherian Modules
Artinian and Noetherian Rings
Hilbert Basis Theorem
Wedderburn-Artin Theorem
Uniform Modules, Primary Modules, and Nother-Lasker Theorem
Module 4
Smith Normal form over a PID and rank
Smith Normal Form
Proof of Smith Normal Form
Uniqueness of Smith Normal Form
Module 5
Modules over PID
Finitely generated modules over PID(Elementary divisor form; Uniqueness)
Rational Canonical Form
Generalized Jordan form over any field
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