Media Storage Type : 64 GB USB Stick
NPTEL Subject Matter Expert : Prof. Dilip P. Patil
NPTEL Co-ordinating Institute : IIT Bombay
NPTEL Lecture Count : 60
NPTEL Course Size : 34 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Zariski Topology and K-Spectrum
Lecture 2 - Algebraic Varieties and Classical Nullstelensatz
Lecture 3 - Motivation for Krulls Dimension
Lecture 4 - Chevalleys dimension
Lecture 5 - Associated Prime Ideals of a Module
Lecture 6 - Support of a Module
Lecture 7 - Primary Decomposition
Lecture 8 - Primary Decomposition (Continued...)
Lecture 9 - Uniqueness of Primary Decomposition
Lecture 10 - Modules of Finite Length
Lecture 11 - Modules of Finite Length (Continued...)
Lecture 12 - Introduction to Krull’s Dimension
Lecture 13 - Noether Normalization Lemma (Classical Version)
Lecture 14 - Consequences of Noether Normalization Lemma
Lecture 15 - Nil Radical and Jacobson Radical of Finite type Algebras over a Field and digression of Integral Extension
Lecture 16 - Nagata’s version of NNL
Lecture 17 - Dimensions of Polynomial ring over Noetherian rings
Lecture 18 - Dimension of Polynomial Algebra over arbitrary Rings
Lecture 19 - Dimension Inequalities
Lecture 20 - Hilbert’s Nullstelensatz
Lecture 21 - Computational rules for Poincaré Series
Lecture 22 - Graded Rings, Modules and Poincaré Series
Lecture 23 - Hilbert-Samuel Polynomials
Lecture 24 - Hilbert-Samuel Polynomials (Continued...)
Lecture 25 - Numerical Function of polynomial type
Lecture 26 - Hilbert-Samuel Polynomial of a Local ring
Lecture 27 - Filtration on a Module
Lecture 28 - Artin-Rees Lemma
Lecture 29 - Dimension Theorem
Lecture 30 - Dimension Theorem (Continued...)
Lecture 31 - Consequences of Dimension Theorem
Lecture 32 - Generalized Krull’s Principal Ideal Theorem
Lecture 33 - Second proof of Krull’s Principal Ideal Theorem
Lecture 34 - The Spec Functor
Lecture 35 - Prime ideals in Polynomial rings
Lecture 36 - Characterization of Equidimensional Affine Algebra
Lecture 37 - Connection between Regular local rings and associated graded rings
Lecture 38 - Statement of the Jacobian Criterion for Regularity
Lecture 39 - Hilbert function for Affine Algebra
Lecture 40 - Hilbert Serre Theorem
Lecture 41 - Jacobian Matrix and its Rank
Lecture 42 - Jacobian Matrix and its Rank (Continued...)
Lecture 43 - Proof of Jacobian Critrerion
Lecture 44 - Proof of Jacobian Critrerion (Continued...)
Lecture 45 - Preparation for Homological Dimension
Lecture 46 - Complexes of Modules and Homology
Lecture 47 - Projective Modules
Lecture 48 - Homological Dimension and Projective module
Lecture 49 - Global Dimension
Lecture 50 - Homological characterization of Regular Local Rings (RLR)
Lecture 51 - Homological characterization of Regular Local Rings (Continued...)
Lecture 52 - Homological Characterization of Regular Local Rings (Continued...)
Lecture 53 - Regular Local Rings are UFD
Lecture 54 - RLR-Prime ideals of height 1
Lecture 55 - Discrete Valuation Ring
Lecture 56 - Discrete Valuation Ring (Continued...)
Lecture 57 - Dedekind Domains
Lecture 58 - Fractionary Ideals and Dedekind Domains
Lecture 59 - Characterization of Dedekind Domain
Lecture 60 - Dedekind Domains and prime factorization of ideals