Modules / Lectures


Sl.No Chapter Name MP4 Download
1Lecture-1:Introduction to RingsDownload
2Lecture-2: Rings, Subrings.Download
3Lecture-3:Ring Homomorphism, Ideals.Download
4Lecture-4:Properties of Ideals.Download
5Lecture-5:Properties of Ideals (contd.)Download
6Lecture-06: Quotient Ring, Isomorphism TheoremDownload
7Lecture-07:Isomorphism Theorem, Homomorphism TheoremDownload
8Lecture-08: Homomorphism TheoremDownload
9Lecture-09: Integral Domain, Quotient RingDownload
10Lecture-10: Quotient RingDownload
11Lecture-11: Prime ideals, Maximal idealsDownload
12Lecture-12: Maximal idealsDownload
13Lecture-13: Hillbert’s NullstellensatzDownload
14Lecture-14: Hillbert’s Nullstellensatz (contd.)Download
15Lecture-15 : Application of Hillbert’s NullstellensatzDownload
16Lecture-16: Unique Factorization domianDownload
17Lecture-17: Properties of Unique Factorization domainDownload
18Lecture-18: Principal ideal domain.Download
19Lecture-19: Properties of PID and EDDownload
20Lecture-20: Properties of PID and ED(contd.)Download
21Lecture-21: Prime elements of Z[i]Download
22Lecture-22: Prime elements of Z[i] (contd.)Download
23Lecture-23: Application in Z[i]Download
24Lecture-24 : Polynomial Rings over UFDDownload
25Lecture-25 : Gauss's LemmaDownload
26Lecture-26: Polynomial Ring over UFD and Irreducibility CriterionDownload
27Lecture-27: Irreducibility CriterionDownload
28Lecture-28: Chinese Remainder TheoremDownload
29Lecture-29: Nilradical and Jacobson radicalDownload
30Lecture-30: Examples and ProblemsDownload
31Lecture-31 : Definition of Modules and ExamplesDownload
32Lecture-32: Definition of Modules and Examples(contd.)Download
33Lecture-33: Submodules,direct sum and direct product of modulesDownload
34Lecture-34 : Direct sum and direct product of modules,free modulesDownload
35Lecture-35 : Finitely generated modules, free modules vs Vector spacesDownload
36Lecture-36: free modules vs Vector spacesDownload
37Lecture-37: Vector spaces vs free modules & Examples.Download
38Lecture -38: Quotient modules and module homomorphisms.Download
39Lecture-39: Module homomorphism , Epimorphism theoremDownload
40Lecture-40: Epimorphism theorem.Download
41Lecture-41: Maximal submodules, minimal submodulesDownload
42Lecture-42: Freeness of submodules of a free module over a PIDDownload
43Lecture-43: Torsion modules, freeness of torsion-free modules over a PIDDownload
44Lecture-44: Rank of a module, p-submodules over a PIDDownload
45Lecture-45: Structure of a torsion module over a PIDDownload
46Lecture-46: Structure theorem, chain conditionsDownload
47Lecture-47: Artinian modules, Artinian ringsDownload
48Lecture-48: Noetherian modules, Noetherian ringsDownload
49Lecture-49: Ascending chain condition, Noetherian modulesDownload
50Lecture-50: Examples of Noetherian and Artinian modules and ringsDownload

Sl.No Chapter Name English
1Lecture-1:Introduction to RingsDownload
Verified
2Lecture-2: Rings, Subrings.Download
Verified
3Lecture-3:Ring Homomorphism, Ideals.PDF unavailable
4Lecture-4:Properties of Ideals.PDF unavailable
5Lecture-5:Properties of Ideals (contd.)PDF unavailable
6Lecture-06: Quotient Ring, Isomorphism TheoremPDF unavailable
7Lecture-07:Isomorphism Theorem, Homomorphism TheoremPDF unavailable
8Lecture-08: Homomorphism TheoremPDF unavailable
9Lecture-09: Integral Domain, Quotient RingPDF unavailable
10Lecture-10: Quotient RingPDF unavailable
11Lecture-11: Prime ideals, Maximal idealsPDF unavailable
12Lecture-12: Maximal idealsPDF unavailable
13Lecture-13: Hillbert’s NullstellensatzPDF unavailable
14Lecture-14: Hillbert’s Nullstellensatz (contd.)PDF unavailable
15Lecture-15 : Application of Hillbert’s NullstellensatzPDF unavailable
16Lecture-16: Unique Factorization domianPDF unavailable
17Lecture-17: Properties of Unique Factorization domainPDF unavailable
18Lecture-18: Principal ideal domain.PDF unavailable
19Lecture-19: Properties of PID and EDPDF unavailable
20Lecture-20: Properties of PID and ED(contd.)PDF unavailable
21Lecture-21: Prime elements of Z[i]PDF unavailable
22Lecture-22: Prime elements of Z[i] (contd.)PDF unavailable
23Lecture-23: Application in Z[i]PDF unavailable
24Lecture-24 : Polynomial Rings over UFDPDF unavailable
25Lecture-25 : Gauss's LemmaPDF unavailable
26Lecture-26: Polynomial Ring over UFD and Irreducibility CriterionPDF unavailable
27Lecture-27: Irreducibility CriterionPDF unavailable
28Lecture-28: Chinese Remainder TheoremPDF unavailable
29Lecture-29: Nilradical and Jacobson radicalPDF unavailable
30Lecture-30: Examples and ProblemsPDF unavailable
31Lecture-31 : Definition of Modules and ExamplesPDF unavailable
32Lecture-32: Definition of Modules and Examples(contd.)PDF unavailable
33Lecture-33: Submodules,direct sum and direct product of modulesPDF unavailable
34Lecture-34 : Direct sum and direct product of modules,free modulesPDF unavailable
35Lecture-35 : Finitely generated modules, free modules vs Vector spacesPDF unavailable
36Lecture-36: free modules vs Vector spacesPDF unavailable
37Lecture-37: Vector spaces vs free modules & Examples.PDF unavailable
38Lecture -38: Quotient modules and module homomorphisms.PDF unavailable
39Lecture-39: Module homomorphism , Epimorphism theoremPDF unavailable
40Lecture-40: Epimorphism theorem.PDF unavailable
41Lecture-41: Maximal submodules, minimal submodulesPDF unavailable
42Lecture-42: Freeness of submodules of a free module over a PIDPDF unavailable
43Lecture-43: Torsion modules, freeness of torsion-free modules over a PIDPDF unavailable
44Lecture-44: Rank of a module, p-submodules over a PIDPDF unavailable
45Lecture-45: Structure of a torsion module over a PIDPDF unavailable
46Lecture-46: Structure theorem, chain conditionsPDF unavailable
47Lecture-47: Artinian modules, Artinian ringsPDF unavailable
48Lecture-48: Noetherian modules, Noetherian ringsPDF unavailable
49Lecture-49: Ascending chain condition, Noetherian modulesPDF unavailable
50Lecture-50: Examples of Noetherian and Artinian modules and ringsPDF unavailable


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