Rings and Modules PF20M9ZPKJ

URI	`m2://res/PF20M9ZPKJ`
Kind	course
Creators	Mousumi Mandal (instructor), Ramakrishna Nanduri (instructor)
Date	2022-06-27
Scope	in
Ids	course 03w5sq511:111105161

Expressions

e1: edition

Language	en
Date	2022-06-27

m1: page, IIT Kharagpur (record). nptel 111105161
m2: page, 2022-06-27 (record). nptel 111105161

Contents

part 1: Week 1
session 1: Lecture-1 : Introduction to Rings
session 2: Lecture-2 : Rings, Subrings
session 3: Lecture-3 : Ring Homomorphism, Ideals
session 4: Lecture-4 : Properties of Ideals
session 5: Lecture-5 : Properties of Ideals(contd.)
part 2: Week 2
session 6: Lecture-6 : Quotient Ring, Isomorphism Theorem
session 7: Lecture-7 : Isomorphism Theorem, Homomorphism Theorem
session 8: Lecture-8 : Homomorphism Theorem
session 9: Lecture-9 : Integral Domain, Quotient Ring
session 10: Lecture-10 : Quotient Ring
part 3: Week 3
session 11: Lecture-11 : Prime ideals, Maximal ideals
session 12: Lecture-12 : Maximal ideals
session 13: Lecture-13 : Hillbert’s Nullstellensatz
session 14: Lecture-14 : Hillbert’s Nullstellensatz (contd.)
session 15: Lecture-15 : Application of Hillbert’s Nullstellensatz
part 4: Week 4
session 16: Lecture-16 : Unique Factorization domian
session 17: Lecture-17 : Properties of Unique Factorization domain
session 18: Lecture-18 : Principal ideal domain
session 19: Lecture-19 : Properties of PID and ED
session 20: Lecture-20 : Properties of PID and ED(contd.)
part 5: Week 5
session 21: Lecture-21 : Prime elements of Z[i]
session 22: Lecture-22 : Prime elements of Z[i] (contd.)
session 23: Lecture-23 : Application in Z[i]
session 24: Lecture-24 : Polynomial Rings over UFD
session 25: Lecture-25 : Gauss's Lemma
part 6: Week 6
session 26: Lecture-26: Polynomial Ring over UFD and Irreducibility Criterion
session 27: Lecture-27 : Irreducibility Criterion
session 28: Lecture-28 : Chinese Remainder Theorem
session 29: Lecture-29 : Nilradical and Jacobson radical
session 30: Lecture-30 : Examples and Problems
part 7: Week 7
session 31: Lecture-31 : Definition of Modules and Examples
session 32: Lecture-32 : Definition of Modules and Examples(contd.)
session 33: Lecture-33 : Submodules,direct sum and direct product of modules
session 34: Lecture-34 : Direct sum and direct product of modules, free modules
session 35: Lecture-35 : Finitely generated modules, free modules vs Vector spaces
part 8: Week 8
session 36: Lecture-36 : free modules vs Vector spaces
session 37: Lecture-37 : Vector spaces vs free modules & Examples
session 38: Lecture-38 : Quotient modules and module homomorphisms
session 39: Lecture-39 : Module homomorphism , Epimorphism theorem
session 40: Lecture-40 : Epimorphism theorem
part 9: Week 9
session 41: Lecture-41 : Maximal submodules, minimal submodules
session 42: Lecture-42 : Freeness of submodules of a free module over a PID
session 43: Lecture-43 : Torsion modules, freeness of torsion-free modules over a PID
session 44: Lecture-44 : Rank of a module, p-submodules over a PID
session 45: Lecture-45 : Structure of a torsion module over a PID
part 10: Week 10
session 46: Lecture-46 : Structure theorem, chain conditions
session 47: Lecture-47 : Artinian modules, Artinian rings
session 48: Lecture-48 : Noetherian modules, Noetherian rings
session 49: Lecture-49 : Ascending chain condition, Noetherian modules
session 50: Lecture-50 : Examples of Noetherian and Artinian modules and rings
part 11: Week 11
session 51: Lecture-51 : Composition series, Modules of finite length
session 52: Lecture-52 : Jordan-Holder’s theorem
session 53: Lecture-53 : Artinian rings
session 54: Lecture-54 : Noetherian rings
session 55: Lecture-55 : Hilbert basis theorem
part 12: Week 12
session 56: Lecture-56 : Cohen’s theorem on Noetherianness
session 57: Lecture-57 : Nakayama lemma
session 58: Lecture-58 : Nil and Jacobson radicals in Artinian rings
session 59: Lecture-59 : Structure theorem
session 60: Lecture-60 : Comparison between Artinian & Noetherian rings

Catalogue records

nptel: 111105161 (manifestation)
nptel_video: 111105161 (manifestation)