Learn · Introduction To Rings And Fields
Lecture 20 of 44Week 4
Field of fractions, Noetherian rings 1
Prof. Krishna Hanumanthu · Chennai Mathematical Institute
Credits and licence
- From
- Introduction To Rings And Fields, Chennai Mathematical Institute (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures
- Introduction, main definitions
- Examples of rings.
- More examples
- Polynomial rings 1
- Polynomial rings 2
- Homomorphisms
- Kernels, ideals
- Problems 1
- Problems 2
- Problems 3
- Quotient rings
- First isomorphism and correspondence theorems
- Examples of correspondence theorem
- Prime ideals
- Maximal ideals, integral domains
- Existence of maximal ideals
- Problems 4
- Problems 5
- Problems 6
- Field of fractions, Noetherian rings 1
- Noetherian rings 2
- Hilbert Basis Theorem
- Irreducible, prime elements
- Irreducible, prime elements, GCD
- Principal Ideal Domains
- Unique Factorization Domains 1
- Unique Factorization Domains 2
- Gauss Lemma
- Z[X] is a UFD
- Eisenstein criterion and Problems 7
- Problems 8
- Problems 9
- Field extensions 1
- Field extensions 2
- Degree of a field extension 1
- Degree of a field extension 2
- Algebraic elements form a field
- Field homomorphisms
- Splitting fields
- Finite fields 1
- Finite fields 2
- Finite fields 3
- Problems 10
- Problems 11