Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Ramakrishna Nanduri, Prof. Mousumi Mandal
NPTEL Co-ordinating Institute : IIT Kharagpur
NPTEL Lecture Count : 60
NPTEL Course Size : 4.1 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Introduction to Rings
Lecture 2 - Rings, Subrings
Lecture 3 - Ring Homomorphism, Ideals
Lecture 4 - Properties of Ideals
Lecture 5 - Properties of Ideals (Continued...)
Lecture 6 - Quotient Ring, Isomorphism Theorem
Lecture 7 - Isomorphism Theorem, Homomorphism Theorem
Lecture 8 - Homomorphism Theorem
Lecture 9 - Integral Domain, Quotient Ring
Lecture 10 - Quotient Ring
Lecture 11 - Prime ideals, Maximal ideals
Lecture 12 - Maximal ideals
Lecture 13 - Hillbert’s Nullstellensatz
Lecture 14 - Hillbert’s Nullstellensatz (Continued...)
Lecture 15 - Application of Hillbert’s Nullstellensatz
Lecture 16 - Unique Factorization domian
Lecture 17 - Properties of Unique Factorization domain
Lecture 18 - Principal ideal domain
Lecture 19 - Properties of PID and ED
Lecture 20 - Properties of PID and ED (Continued...)
Lecture 21 - Prime elements of Z[i]
Lecture 22 - Prime elements of Z[i] (Continued...)
Lecture 23 - Application in Z[i]
Lecture 24 - Polynomial Rings over UFD
Lecture 25 - Gauss's Lemma
Lecture 26 - Polynomial Ring over UFD and Irreducibility Criterion
Lecture 27 - Irreducibility Criterion
Lecture 28 - Chinese Remainder Theorem
Lecture 29 - Nilradical and Jacobson radical
Lecture 30 - Examples and Problems
Lecture 31 - Definition of Modules and Examples
Lecture 32 - Definition of Modules and Examples (Continued...)
Lecture 33 - Submodules,direct sum and direct product of modules
Lecture 34 - Direct sum and direct product of modules, free modules
Lecture 35 - Finitely generated modules, free modules vs Vector spaces
Lecture 36 - Free modules vs Vector spaces
Lecture 37 - Vector spaces vs free modules and Examples
Lecture 38 - Quotient modules and module homomorphisms
Lecture 39 - Module homomorphism, Epimorphism theorem
Lecture 40 - Epimorphism theorem
Lecture 41 - Maximal submodules, minimal submodules
Lecture 42 - Freeness of submodules of a free module over a PID
Lecture 43 - Torsion modules, freeness of torsion-free modules over a PID
Lecture 44 - Rank of a module, p-submodules over a PID
Lecture 45 - Structure of a torsion module over a PID
Lecture 46 - Structure theorem, chain conditions
Lecture 47 - Artinian modules, Artinian rings
Lecture 48 - Noetherian modules, Noetherian rings
Lecture 49 - Ascending chain condition, Noetherian modules
Lecture 50 - Examples of Noetherian and Artinian modules and rings
Lecture 51 - Composition series, Modules of finite length
Lecture 52 - Jordan-Holderâ's theorem
Lecture 53 - Artinian rings
Lecture 54 - Noetherian rings
Lecture 55 - Hilbert basis theorem
Lecture 56 - Cohenâ's theorem on Noetherianness
Lecture 57 - Nakayama lemma
Lecture 58 - Nil and Jacobson radicals in Artinian rings
Lecture 59 - Structure theorem
Lecture 60 - Comparison between Artinian and Noetherian rings