Introduction to Algebraic Geometry and Commutative Algebra 2GZSQHVRF7

URI	`m2://res/2GZSQHVRF7`
Kind	course
Creators	Dilip P. Patil (instructor)
Date	2019-12-16
MSC	14-XX
Scope	in
Ids	course 04dese585:111108136

Expressions

e1: edition

Language	en
Date	2019-12-16

m1: page, IISc Bangalore (record). nptel 111108136
m2: page, 2019-12-16 (record). nptel 111108136

Contents

part 1: Week 1 Algebraic Preliminaries 1- Rings and Ideals
session 1: Motivation for K-algebraic sets
session 2: Definitions and examples of Affine Algebraic Set
session 3: Rings and Ideals
session 4: Operation on Ideals
session 5: Prime Ideals and Maximal Ideals
part 2: Week 2 Algebraic Preliminaries 2-Modules and Algebras
session 6: Krull's Theorem and consequences
session 7: Module, submodules and quotient modules
session 8: Algebras and polynomial algebras
session 9: Universal property of polynomial algebra and examples
session 10: Finite and Finite type algebras
part 3: Week 3 The K-Spectrum of a K-algebra and Affine algebraic sets
session 11: K-Spectrum (K-rational points)
session 12: Identity theorem for Polynomial functions
session 13: Basic properties of K-algebraic sets
session 14: Examples of K-algebraic sets
session 15: K-Zariski Topology
part 4: Week 4 Noetherian and Artinian Modules
session 16: The map V L
session 17: Noetherian and Artinian Ordered sets
session 18: Noetherian induction and Transfinite induction
session 19: Modules with Chain Conditions
session 20: Properties of Noetherian and Artinian Modules
part 5: Week 5 Hilbert’s Basis Theorem and consequences
session 21: Examples of Artinian and Noetherian Modules
session 22: Finite modules over Noetherian Rings
session 23: Hilbert's Basis Theorem(HBT)
session 24: Consequences of HBT
session 25: Free Modules and rank
part 6: Week 6 Rings of Fractions
session 26: More on Noetherian and Artinian modules
session 27: Ring of Fractions(Localization)
session 28: Nil radical, contraction of ideals
session 29: Universal property of S -1 A
session 30: Ideal structure in S -1 A
part 7: Week 7 Modules of fractions
session 31: Consequences of the Correspondence of Ideals
session 32: Consequences of the Correspondence of Ideals(Contd.)
session 33: Modules of Fraction and universal properties
session 34: Exactness of the functor S -1
session 35: Universal property of Modules of Fractions
part 8: Week 8 Local Global Principle and Consequences
session 36: Further properties of Modules and Module of Fractions
session 37: Local-Global Principle
session 38: Consequences of Local-Global Principle
session 39: Properties of Artinian Rings
session 40: Krull-Nakayama Lemma
part 9: Week 9 Hilbert's Nullstellensatz and its equivalent formulations
session 41: Properties of I K and V L maps
session 42: Hilbert's Nullstelensatz
session 43: Hilbert's Nullstelensatz(Contd.)
session 44: Proof of Zariski's Lemma(HNS 3)
session 45: Consequences of HNS
part 10: Week 10 Consequences of HNS
session 46: Consequences of HNS(Contd.)
session 47: Jacobson Ring and examples
session 48: Irreducible subsets of Zariski Topology(Finite type K-algebra)
session 49: Spec functor on Finite type K-algebras
session 50: Properties of Irreducible topological spaces
part 11: Week 11 Zariski Topology
session 51: Zariski Topology on arbitrary commutative rings
session 52: Spec functor on arbitrary commutative rings
session 53: Topological properties of Spec A
session 54: Example to support the term Spectrum-
session 55: Integral Extensions
part 12: Week 12 Integral Extensions
session 56: Elementwise characterization of Integral extensions
session 57: Properties and examples of Integral extensions
session 58: Prime and Maximal ideals in integral extensions
session 59: Lying over Theorem
session 60: Cohen-Siedelberg Theorem
part 13: Live Session
session 61: Live Session 17-03-2022
session 62: Live Session 03-03-2025

Catalogue records

nptel: 111108136 (manifestation)
nptel_video: 111108136 (manifestation)