Commutative Algebra Y6YW6RAMC0

URI	`m2://res/Y6YW6RAMC0`
Kind	course
Creators	Dilip P. Patil (instructor)
Date	2018-12-23
Scope	in
Ids	course 02qyf5152:111101116

Expressions

e1: edition

Language	en
Date	2018-12-23

m1: page, IIT Bombay (record). nptel 111101116
m2: page, 2018-12-23 (record). nptel 111101116

Contents

part 1: Week 1
session 1: Lecture 1 : Zariski Topology and K-Spectrum
session 2: Lecture 2 : Algebraic Varieties and Classical Nullstelensatz
session 3: Lecture 3 : Motivation for Krulls Dimension
session 4: Lecture 4 : Chevalleys dimension
session 5: Lecture 5 : Associated Prime Ideals of a Module
part 2: Week 2
session 6: Lecture 6 : Support of a Module
session 7: Lecture 7 : Primary Decomposition
session 8: Lecture 8 : Primary Decomposition(Contd)
session 9: Lecture 9 : Uniqueness of Primary Decomposition
session 10: Lecture 10 : Modules of Finite Length
part 3: Week 3
session 11: Lecture 11 : Modules of Finite Length(Contd)
session 12: Lecture 12 : Introduction to Krull's Dimension
session 13: Lecture 13 : Noether Normalization Lemma(Classical Version)
session 14: Lecture 14 : Consequences of Noether Normalization Lemma
session 15: Lecture 15 : Nil Radical and Jacobson Radical of Finite type Algebras over a Field and digression of Integral Extension
part 4: Week 4
session 16: Lecture 16 : Nagata's version of NNL
session 17: Lecture 17 : Dimensions of Polynomial ring over Noetherian rings
session 18: Lecture 18 : Dimension of Polynomial Algebra over arbitrary Rings
session 19: Lecture 19 : Dimension Inequalities
session 20: Lecture 20 : Hilbert's Nullstelensatz
part 5: Week 5
session 23: Lecture 23 : Hilbert-Samuel Polynomials
session 24: Lecture 24 : Hilbert-Samuel Polynomials(Contd)
session 25: Lecture 25 : Numerical Function of polynomial type
part 6: Week 6
session 26: Lecture 26 : Hilbert-Samuel Polynomial of a Local ring
session 27: Lecture 27 : Filtration on a Module
session 28: Lecture 28 : Artin-Rees Lemma
session 29: Lecture 29 : Dimension Theorem
session 30: Lecture 30 : Dimension Theorem(Continued)
part 7: Week 7
session 31: Lecture 31 : Consequences of Dimension Theorem
session 32: Lecture 32 : Generalized Krull's Principal Ideal Theorem
session 33: Lecture 33 : Second proof of Krull's Principal Ideal Theorem
session 34: Lecture 34 : The Spec Functor
session 35: Lecture 35 : Prime ideals in Polynomial rings
part 8: Week 8
session 36: Lecture 36 : Characterization of Equidimensional Affine Algebra
session 37: Lecture 37 : Connection between Regular local rings and associated graded rings
session 38: Lecture 38 : Statement of the Jacobian Criterion for Regularity
session 39: Lecture 39 : Hilbert function for Affine Algebra
session 40: Lecture 40 : Hilbert Serre Theorem
part 9: Week 9
session 41: Lecture 41 : Jacobian Matrix and its Rank
session 42: Lecture 42 : Jacobian Matrix and its Rank(Contd)
session 43: Lecture 43 : Proof of Jacobian Critrerion
session 44: Lecture 44 : Proof of Jacobian Critrerion(Contd)
session 45: Lecture 45 : Preparation for Homological Dimension
part 10: Week 10
session 46: Lecture 46 : Complexes of Modules and Homology
session 47: Lecture 47 : Projective Modules
session 48: Lecture 48 : Homological Dimension and Projective module
session 49: Lecture 49 : Global Dimension
session 50: Lecture 50 : Homological characterization of Regular Local Ring(RLR)
part 11: Week 11
session 51: Lecture 51 : Homological characterization of Regular Local Ring(Contd)
session 52: Lecture 52 : Homological Characterization of Regular Local Rings(Contd)
session 53: Lecture 53 : Regular Local Rings are UFD
session 54: Lecture 54 : RLR-Prime ideals of height 1
session 55: Lecture 55 : Discrete Valuation Ring
part 12: Week 12
session 56: Lecture 56 : Discrete Valuation Ring(Contd)
session 57: Lecture 57 : Dedekind Domains
session 58: Lecture 58 : Fractionary Ideals and Dedekind Domains
session 59: Lecture 59 : Characterization of Dedekind Domain
session 60: Lecture 60 : Dedekind Domains and prime factorization of ideals

Catalogue records

nptel: 111101116 (manifestation)
nptel_video: 111101116 (manifestation)