Introduction To Rings And Fields G4JQME7EXH

URI	`m2://res/G4JQME7EXH`
Kind	course
Creators	Krishna Hanumanthu (instructor)
Date	2019-08-23
Scope	in

Expressions

e1: edition

Language	en
Date	2019-08-23

m1: page, Chennai Mathematical Institute (record). nptel 111106131
m2: page, 2019-08-23 (record). nptel 111106131

Contents

part 1: Week 1
session 1: Introduction, main definitions
session 2: Examples of rings.
session 3: More examples
session 4: Polynomial rings 1
session 5: Polynomial rings 2
part 2: Week 2
session 6: Homomorphisms
session 7: Kernels, ideals
session 8: Problems 1
session 9: Problems 2
session 10: Problems 3
part 3: Week 3
session 11: Quotient rings
session 12: First isomorphism and correspondence theorems
session 13: Examples of correspondence theorem
session 14: Prime ideals
session 15: Maximal ideals, integral domains
part 4: Week 4
session 16: Existence of maximal ideals
session 17: Problems 4
session 18: Problems 5
session 19: Problems 6
session 20: Field of fractions, Noetherian rings 1
session 21: Noetherian rings 2
part 5: Week 5
session 22: Hilbert Basis Theorem
session 23: Irreducible, prime elements
session 24: Irreducible, prime elements, GCD
session 25: Principal Ideal Domains
session 26: Unique Factorization Domains 1
session 27: Unique Factorization Domains 2
part 6: Week 6
session 28: Gauss Lemma
session 29: Z[X] is a UFD
session 30: Eisenstein criterion and Problems 7
session 31: Problems 8
session 32: Problems 9
part 7: Week 7
session 33: Field extensions 1
session 34: Field extensions 2
session 35: Degree of a field extension 1
session 36: Degree of a field extension 2
session 37: Algebraic elements form a field
session 38: Field homomorphisms
part 8: Week 8
session 39: Splitting fields
session 40: Finite fields 1
session 41: Finite fields 2
session 42: Finite fields 3
session 43: Problems 10
session 44: Problems 11

Catalogue records

nptel: 111106131 (manifestation)
nptel_video: 111106131 (manifestation)