Modules / Lectures
Module NameDownload
noc19_ma16-assessmentid-106noc19_ma16-assessmentid-106
noc19_ma16-assessmentid-110noc19_ma16-assessmentid-110
noc19_ma16-assessmentid-114noc19_ma16-assessmentid-114
noc19_ma16-assessmentid-122noc19_ma16-assessmentid-122
noc19_ma16-assessmentid-123noc19_ma16-assessmentid-123
noc19_ma16-assessmentid-126noc19_ma16-assessmentid-126
noc19_ma16-assessmentid-8noc19_ma16-assessmentid-8
noc19_ma16-assessmentid-81noc19_ma16-assessmentid-81
noc19_ma16-assessmentid-96noc19_ma16-assessmentid-96
noc19_ma16-assessmentid-97noc19_ma16-assessmentid-97
noc19_ma16-assessmentid-99noc19_ma16-assessmentid-99

Sl.No Chapter Name English
1Lecture 1 : Zariski Topology and K-SpectrumDownload
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2Lecture 2 : Algebraic Varieties and Classical NullstelensatzDownload
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3Lecture 3 : Motivation for Krulls DimensionDownload
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4Lecture 4 : Chevalleys dimensionDownload
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5Lecture 5 : Associated Prime Ideals of a ModuleDownload
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6Lecture 6 : Support of a ModuleDownload
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7Lecture 7 : Primary DecompositionDownload
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8Lecture 8 : Primary Decomposition(Contd)Download
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9Lecture 9 : Uniqueness of Primary DecompositionDownload
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10Lecture 10 : Modules of Finite LengthDownload
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11Lecture 11 : Modules of Finite Length(Contd)Download
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12Lecture 12 : Introduction to Krull’s DimensionDownload
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13Lecture 13 : Noether Normalization Lemma(Classical Version)Download
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14Lecture 14 : Consequences of Noether Normalization LemmaDownload
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15Lecture 15 : Nil Radical and Jacobson Radical of Finite type Algebras over a Field and digression of Integral ExtensionDownload
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16Lecture 16 : Nagata’s version of NNLDownload
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17Lecture 17 : Dimensions of Polynomial ring over Noetherian ringsDownload
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18Lecture 18 : Dimension of Polynomial Algebra over arbitrary RingsDownload
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19Lecture 19 : Dimension InequalitiesDownload
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20Lecture 20 : Hilbert’s NullstelensatzDownload
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21Lecture 21 : Computational rules for Poincaré SeriesDownload
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22Lecture 22 : Graded Rings, Modules and Poincaré SeriesDownload
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23Lecture 23 : Hilbert-Samuel PolynomialsDownload
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24Lecture 24 : Hilbert-Samuel Polynomials(Contd)Download
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25Lecture 25 : Numerical Function of polynomial typeDownload
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26Lecture 26 : Hilbert-Samuel Polynomial of a Local ringDownload
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27Lecture 27 : Filtration on a ModuleDownload
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28Lecture 28 : Artin-Rees LemmaDownload
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29Lecture 29 : Dimension TheoremDownload
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30Lecture 30 : Dimension Theorem(Continued)Download
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31Lecture 31 : Consequences of Dimension TheoremDownload
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32Lecture 32 : Generalized Krull’s Principal Ideal TheoremDownload
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33Lecture 33 : Second proof of Krull’s Principal Ideal TheoremDownload
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34Lecture 34 : The Spec FunctorDownload
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35Lecture 35 : Prime ideals in Polynomial ringsDownload
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36Lecture 36 : Characterization of Equidimensional Affine AlgebraDownload
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37Lecture 37 : Connection between Regular local rings and associated graded ringsDownload
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38Lecture 38 : Statement of the Jacobian Criterion for RegularityDownload
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39Lecture 39 : Hilbert function for Affine AlgebraDownload
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40Lecture 40 : Hilbert Serre TheoremDownload
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41Lecture 41 : Jacobian Matrix and its RankDownload
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42Lecture 42 : Jacobian Matrix and its Rank(Contd)Download
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43Lecture 43 : Proof of Jacobian CritrerionDownload
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44Lecture 44 : Proof of Jacobian Critrerion(Contd)Download
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45Lecture 45 : Preparation for Homological DimensionDownload
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46Lecture 46 : Complexes of Modules and HomologyDownload
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47Lecture 47 : Projective ModulesDownload
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48Lecture 48 : Homological Dimension and Projective moduleDownload
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49Lecture 49 : Global DimensionDownload
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50Lecture 50 : Homological characterization of Regular Local Ring(RLR)Download
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51Lecture 51 : Homological characterization of Regular Local Ring(Contd)Download
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52Lecture 52 : Homological Characterization of Regular Local Rings(Contd)Download
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53Lecture 53 : Regular Local Rings are UFDDownload
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54Lecture 54 : RLR-Prime ideals of height 1Download
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55Lecture 55 : Discrete Valuation RingDownload
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56Lecture 56 : Discrete Valuation Ring(Contd)Download
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57Lecture 57 : Dedekind DomainsDownload
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58Lecture 58 : Fractionary Ideals and Dedekind DomainsDownload
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59Lecture 59 : Characterization of Dedekind DomainDownload
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60Lecture 60 : Dedekind Domains and prime factorization of idealsDownload
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1EnglishDownload
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available