Introduction to rings – Youtube lectures (Hebrew)

These lecture notes correspond to my youtube lecture series which can be found here.

  1. Introduction – definition of rings and examples.
  2. Introduction – basic definitions and properties.
  3. The quaternions – the noncommutative field example.
  4. Subrings and generating sets.
  5. Homomorphisms.
  6. Ideals and quotient rings.
  7. Isomorphism theorems.
  8. The Chinese Remainder Theorem.
  9. Approximating rings.
  10. Maximal ideals.
  11. Fraction fields and prime ideals.
  12. Euclidean domains.
  13. Principal ideal domains.
  14. Unique factorization domains.
  15. Gaussian integers.
  16. Polynomials over unique factorization domains.
  17. Irreducible polynomials.
  18. Polynomials over fields.
  19. Introduction to fields.
  20. Algebraic extensions.
  21. Towers of fields.
  22. Finite fields.
  23. Subfields of finite fields.
  24. The multiplicative group of a field.