Modules / Lectures
Module NameDownload


Sl.No Chapter Name MP4 Download
1Motivation for K-algebraic setsDownload
2Definitions and examples of Affine Algebraic SetDownload
3Rings and IdealsDownload
4Operation on IdealsDownload
5Prime Ideals and Maximal IdealsDownload
6Krull's Theorem and consequencesDownload
7Module, submodules and quotient modulesDownload
8Algebras and polynomial algebrasDownload
9Universal property of polynomial algebra and examplesDownload
10Finite and Finite type algebrasDownload
11K-Spectrum (K-rational points)Download
12Identity theorem for Polynomial functionsDownload
13Basic properties of K-algebraic setsDownload
14Examples of K-algebraic setsDownload
15K-Zariski TopologyDownload
16The map V LDownload
17Noetherian and Artinian Ordered setsDownload
18Noetherian induction and Transfinite inductionDownload
19Modules with Chain ConditionsDownload
20Properties of Noetherian and Artinian ModulesDownload
21Examples of Artinian and Noetherian ModulesDownload
22Finite modules over Noetherian RingsDownload
23Hilbert’s Basis Theorem(HBT)Download
24Consequences of HBTDownload
25Free Modules and rankDownload
26More on Noetherian and Artinian modulesDownload
27Ring of Fractions(Localization)Download
28Nil radical, contraction of idealsDownload
29Universal property of S -1 ADownload
30Ideal structure in S -1 ADownload
31Consequences of the Correspondence of IdealsDownload
32Consequences of the Correspondence of Ideals(Contd.)Download
33Modules of Fraction and universal propertiesDownload
34Exactness of the functor S -1Download
35Universal property of Modules of FractionsDownload
36Further properties of Modules and Module of FractionsDownload
37Local-Global PrincipleDownload
38Consequences of Local-Global PrincipleDownload
39Properties of Artinian RingsDownload
40Krull-Nakayama LemmaDownload
41Properties of I K and V L mapsDownload
42Hilbert’s NullstelensatzDownload
43Hilbert’s Nullstelensatz(Contd.)Download
44Proof of Zariski’s Lemma(HNS 3)Download
45Consequences of HNSDownload
46Consequences of HNS(Contd.)Download
47Jacobson Ring and examplesDownload
48Irreducible subsets of Zariski Topology(Finite type K-algebra)Download
49Spec functor on Finite type K-algebrasDownload
50Properties of Irreducible topological spacesDownload
51Zariski Topology on arbitrary commutative ringsDownload
52Spec functor on arbitrary commutative ringsDownload
53Topological properties of Spec ADownload
54Example to support the term “Spectrum”Download
55Integral ExtensionsDownload
56Elementwise characterization of Integral extensionsDownload
57Properties and examples of Integral extensionsDownload
58Prime and Maximal ideals in integral extensionsDownload
59Lying over TheoremDownload
60Cohen-Siedelberg TheoremDownload

Sl.No Chapter Name English
1Motivation for K-algebraic setsDownload
Verified
2Definitions and examples of Affine Algebraic SetDownload
Verified
3Rings and IdealsDownload
Verified
4Operation on IdealsDownload
Verified
5Prime Ideals and Maximal IdealsDownload
Verified
6Krull's Theorem and consequencesPDF unavailable
7Module, submodules and quotient modulesPDF unavailable
8Algebras and polynomial algebrasPDF unavailable
9Universal property of polynomial algebra and examplesPDF unavailable
10Finite and Finite type algebrasPDF unavailable
11K-Spectrum (K-rational points)PDF unavailable
12Identity theorem for Polynomial functionsPDF unavailable
13Basic properties of K-algebraic setsPDF unavailable
14Examples of K-algebraic setsPDF unavailable
15K-Zariski TopologyPDF unavailable
16The map V LPDF unavailable
17Noetherian and Artinian Ordered setsPDF unavailable
18Noetherian induction and Transfinite inductionPDF unavailable
19Modules with Chain ConditionsPDF unavailable
20Properties of Noetherian and Artinian ModulesPDF unavailable
21Examples of Artinian and Noetherian ModulesPDF unavailable
22Finite modules over Noetherian RingsPDF unavailable
23Hilbert’s Basis Theorem(HBT)PDF unavailable
24Consequences of HBTPDF unavailable
25Free Modules and rankPDF unavailable
26More on Noetherian and Artinian modulesPDF unavailable
27Ring of Fractions(Localization)PDF unavailable
28Nil radical, contraction of idealsPDF unavailable
29Universal property of S -1 APDF unavailable
30Ideal structure in S -1 APDF unavailable
31Consequences of the Correspondence of IdealsPDF unavailable
32Consequences of the Correspondence of Ideals(Contd.)PDF unavailable
33Modules of Fraction and universal propertiesPDF unavailable
34Exactness of the functor S -1PDF unavailable
35Universal property of Modules of FractionsPDF unavailable
36Further properties of Modules and Module of FractionsPDF unavailable
37Local-Global PrinciplePDF unavailable
38Consequences of Local-Global PrinciplePDF unavailable
39Properties of Artinian RingsPDF unavailable
40Krull-Nakayama LemmaPDF unavailable
41Properties of I K and V L mapsPDF unavailable
42Hilbert’s NullstelensatzPDF unavailable
43Hilbert’s Nullstelensatz(Contd.)PDF unavailable
44Proof of Zariski’s Lemma(HNS 3)PDF unavailable
45Consequences of HNSPDF unavailable
46Consequences of HNS(Contd.)PDF unavailable
47Jacobson Ring and examplesPDF unavailable
48Irreducible subsets of Zariski Topology(Finite type K-algebra)PDF unavailable
49Spec functor on Finite type K-algebrasPDF unavailable
50Properties of Irreducible topological spacesPDF unavailable
51Zariski Topology on arbitrary commutative ringsPDF unavailable
52Spec functor on arbitrary commutative ringsPDF unavailable
53Topological properties of Spec APDF unavailable
54Example to support the term “Spectrum”PDF unavailable
55Integral ExtensionsPDF unavailable
56Elementwise characterization of Integral extensionsPDF unavailable
57Properties and examples of Integral extensionsPDF unavailable
58Prime and Maximal ideals in integral extensionsPDF unavailable
59Lying over TheoremPDF unavailable
60Cohen-Siedelberg TheoremPDF unavailable


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