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