NOC:Introduction to Rings and Fields


Lecture 1 - Introduction, main definitions


Lecture 2 - Examples of rings


Lecture 3 - More examples


Lecture 4 - Polynomial Rings - 1


Lecture 5 - Polynomial Rings - 2


Lecture 6 - Homomorphisms


Lecture 7 - Kernels, ideals


Lecture 8 - Problems - 1


Lecture 9 - Problems - 2


Lecture 10 - Problems - 3


Lecture 11 - Quotient Rings


Lecture 12 - First isomorphism and correspondence theorems


Lecture 13 - Examples of correspondence theorem


Lecture 14 - Prime ideals


Lecture 15 - Maximal ideals, integral domains


Lecture 16 - Existence of maximal ideals


Lecture 17 - Problems - 4


Lecture 18 - Problems - 5


Lecture 19 - Problems - 6


Lecture 20 - Field of fractions, Noetherian rings - 1


Lecture 21 - Noetherian rings - 2


Lecture 22 - Hilbert Basis Theorem


Lecture 23 - Irreducible, prime elements


Lecture 24 - Irreducible, prime elements, GCD


Lecture 25 - Principal Ideal Domains


Lecture 26 - Unique Factorization Domains - 1


Lecture 27 - Unique Factorization Domains - 2


Lecture 28 - Gauss Lemma


Lecture 29 - Z[X] is a UFD


Lecture 30 - Eisenstein criterion and Problems - 7


Lecture 31 - Problems - 8


Lecture 32 - Problems - 9


Lecture 33 - Field extensions - 1


Lecture 34 - Field extensions - 2


Lecture 35 - Degree of a field extension - 1


Lecture 36 - Degree of a field extension - 2


Lecture 37 - Algebraic elements form a field


Lecture 38 - Field homomorphisms


Lecture 39 - Splitting fields


Lecture 40 - Finite fields - 1


Lecture 41 - Finite fields - 2


Lecture 42 - Finite fields - 3


Lecture 43 - Problems - 10


Lecture 44 - Problems - 11