Algebra _ II R0BHZ4WRS1

URI	`m2://res/R0BHZ4WRS1`
Kind	course
Creators	Amritanshu Prasad (instructor), S. Viswanath (instructor)
Date	2022-10-11
Scope	in

Expressions

e1: edition

Language	en
Date	2022-10-11

m1: page, IMSc (record). nptel 111106151
m2: page, 2022-10-11 (record). nptel 111106151

Contents

part 1: Week 1
session 1: Algebraic and Transcendental Numbers
session 2: Extensions Generated by Elements
session 3: Isomorphic Extensions
session 4: Degree of an Extension
session 5: Constructible Numbers
session 6: The Field of Constructible Numbers
session 7: Characterization of Constructible Numbers
session 8: Solved Problems (Week 1)
part 2: Week 2
session 9: Some Things can't be Constructed
session 10: Symbolic Adjunction
session 11: Repeated Roots
session 12: Gauss Lemma
session 13: Eisenstein's criterion
session 14: Existence Theorem for Finite Fields
session 15: Subfields of a Finite Field
session 16: Multiplicative Group of a Finite Field
session 17: Uniqueness Theorem for Finite Fields
session 18: Solved Problems (week 2)
part 3: Week 3
session 19: Algebraic Extensions and Algebraic Closures
session 20: Existence of Algebraic Closures
session 21: Uniqueness of Algebraic Closure
session 22: Solved Problems, part 1 (Week 3)
session 23: Existence of splitting fields, bound on degree
session 24: Uniqueness of splitting fields
session 25: Solved problems , part 2 (Week 3)
part 4: Week 4
session 26: Normal Extensions
session 27: Separable polynomials
session 28: Perfect fields, separable extensions
session 29: Definition and examples, fixed fields
session 30: Characterization of Galois extensions
session 31: Linear Independence of Characters
session 32: Solved problems (Week 4)
part 5: Week 5
session 33: Artin's Theorem - part 1
session 34: Artin's Theorem - part 2
session 35: Finite Galois Extensions
session 36: The fundamental theorem of Galois Theory - 1
session 37: The fundamental theorem of Galois Theory - 2
session 38: Solved problems (Week 5)
part 6: Week 6
session 39: Cyclotomic extensions
session 40: Irreducibility of the cyclotomic polynomial
session 41: Application: Constructibility of regular n-gons.
session 42: Insolvability of the general quintic - part 1
session 43: Insolvability of the general quintic - part 2
session 44: Insolvability of the general quintic - part 3
part 7: Week 7
session 45: What is category theory (and why is it important)?
session 46: Definition of a category
session 47: Monomorphisms, epimorphisms, and isomorphisms
session 48: Categories: First Problem Session
session 49: Initial and Terminal Objects
session 50: Products and Coproducts
session 51: Categories: Second Problem Session
part 8: Week 8
session 52: Functors
session 53: The Category of Categories
session 54: Natural Transformations
session 55: Functor Categories
session 56: Categories: Third Problem Session
session 57: Adjunction
session 58: Categories: Fourth Problem Session
part 9: Week 9
session 59: Tensor products of Z-modules
session 60: Free abelian groups and quotient groups
session 61: Construction of the tensor product
session 62: Problem session
session 63: Tensor product of R-modules
part 10: Week 10
session 64: Functoriality of the tensor product
session 65: Bimodules
session 66: Tensor products of bimodules
session 67: Tensor products of modules over commutative rings
session 68: Extension of scalars
session 69: Problem session - tensor products of vector spaces
part 11: Week 11
session 70: Some Properties of the tensor product
session 71: F-algebras
session 72: Composition Series
session 73: Schreier's Theorem
session 74: Ascending and Descending Chain Conditions
session 75: Existence of Jordan-Holder Series
session 76: The Jordan-Holder Theorem
session 77: Examples related to the Jordan-Holder Theorem
part 12: Week 12
session 78: The Jordan-Holder Theorem for Groups
session 79: Indecomposable Modules
session 80: Direct Sum Decompositions
session 81: Decomposition as a sum of Indecomposables
session 82: The Endomorphism Ring of an Indecomposable Module
session 83: Krull-Schmidt Theorem
session 84: Krull-Schmidt Examples
part 13: Live Session
session 85: Live Session 05-03-2021
session 86: Live Session 03-04-2021

Catalogue records

nptel: 111106151 (manifestation)
nptel_video: 111106151 (manifestation)