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Course11110613144 lectures

Introduction To Rings And Fields

Prof. Krishna Hanumanthu · Chennai Mathematical Institute

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction, main definitions Video
  2. Examples of rings. Video
  3. More examples Video
  4. Polynomial rings 1 Video
  5. Polynomial rings 2 Video

Week 2

  1. Homomorphisms Video
  2. Kernels, ideals Video
  3. Problems 1 Video
  4. Problems 2 Video
  5. Problems 3 Video

Week 3

  1. Quotient rings Video
  2. First isomorphism and correspondence theorems Video
  3. Examples of correspondence theorem Video
  4. Prime ideals Video
  5. Maximal ideals, integral domains Video

Week 4

  1. Existence of maximal ideals Video
  2. Problems 4 Video
  3. Problems 5 Video
  4. Problems 6 Video
  5. Field of fractions, Noetherian rings 1 Video
  6. Noetherian rings 2 Video

Week 5

  1. Hilbert Basis Theorem Video
  2. Irreducible, prime elements Video
  3. Irreducible, prime elements, GCD Video
  4. Principal Ideal Domains Video
  5. Unique Factorization Domains 1 Video
  6. Unique Factorization Domains 2 Video

Week 6

  1. Gauss Lemma Video
  2. Z[X] is a UFD Video
  3. Eisenstein criterion and Problems 7 Video
  4. Problems 8 Video
  5. Problems 9 Video

Week 7

  1. Field extensions 1 Video
  2. Field extensions 2 Video
  3. Degree of a field extension 1 Video
  4. Degree of a field extension 2 Video
  5. Algebraic elements form a field Video
  6. Field homomorphisms Video

Week 8

  1. Splitting fields Video
  2. Finite fields 1 Video
  3. Finite fields 2 Video
  4. Finite fields 3 Video
  5. Problems 10 Video
  6. Problems 11 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Chennai Mathematical Institute
Department
Mathematics
Teacher
Prof. Krishna Hanumanthu
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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