# Introduction To Rings And Fields

- Institution: Chennai Mathematical Institute
- Department: Mathematics
- Teacher: Prof. Krishna Hanumanthu
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106131)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106131)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction, main definitions](https://invisiblenetwork.ai/learn/nptel/111106131/e00e29642c7e) (Video)
2. [Examples of rings.](https://invisiblenetwork.ai/learn/nptel/111106131/19d5a1396695) (Video)
3. [More examples](https://invisiblenetwork.ai/learn/nptel/111106131/941e8145cb03) (Video)
4. [Polynomial rings 1](https://invisiblenetwork.ai/learn/nptel/111106131/1c3ccc4ad8b7) (Video)
5. [Polynomial rings 2](https://invisiblenetwork.ai/learn/nptel/111106131/91df08011b16) (Video)
6. [Homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106131/f85c8a08bd05) (Video)
7. [Kernels, ideals](https://invisiblenetwork.ai/learn/nptel/111106131/5a5b3c70ecec) (Video)
8. [Problems 1](https://invisiblenetwork.ai/learn/nptel/111106131/0a8791035ea2) (Video)
9. [Problems 2](https://invisiblenetwork.ai/learn/nptel/111106131/9245f472c76d) (Video)
10. [Problems 3](https://invisiblenetwork.ai/learn/nptel/111106131/eeec7aab223b) (Video)
11. [Quotient rings](https://invisiblenetwork.ai/learn/nptel/111106131/7b69f92c1640) (Video)
12. [First isomorphism and correspondence theorems](https://invisiblenetwork.ai/learn/nptel/111106131/b1ab8008ef5d) (Video)
13. [Examples of correspondence theorem](https://invisiblenetwork.ai/learn/nptel/111106131/712deea1f4f9) (Video)
14. [Prime ideals](https://invisiblenetwork.ai/learn/nptel/111106131/8e017bd5e7d7) (Video)
15. [Maximal ideals, integral domains](https://invisiblenetwork.ai/learn/nptel/111106131/90987927a60b) (Video)
16. [Existence of maximal ideals](https://invisiblenetwork.ai/learn/nptel/111106131/e5431352f5be) (Video)
17. [Problems 4](https://invisiblenetwork.ai/learn/nptel/111106131/1188bd55fdbd) (Video)
18. [Problems 5](https://invisiblenetwork.ai/learn/nptel/111106131/26e18c23064a) (Video)
19. [Problems 6](https://invisiblenetwork.ai/learn/nptel/111106131/329d41abaf5a) (Video)
20. [Field of fractions, Noetherian rings 1](https://invisiblenetwork.ai/learn/nptel/111106131/ef1045df9b65) (Video)
21. [Noetherian rings 2](https://invisiblenetwork.ai/learn/nptel/111106131/09cad343ea09) (Video)
22. [Hilbert Basis Theorem](https://invisiblenetwork.ai/learn/nptel/111106131/262758b04b17) (Video)
23. [Irreducible, prime elements](https://invisiblenetwork.ai/learn/nptel/111106131/539fcd82b30b) (Video)
24. [Irreducible, prime elements, GCD](https://invisiblenetwork.ai/learn/nptel/111106131/1e89b5874448) (Video)
25. [Principal Ideal Domains](https://invisiblenetwork.ai/learn/nptel/111106131/7adcd35cfa42) (Video)
26. [Unique Factorization Domains 1](https://invisiblenetwork.ai/learn/nptel/111106131/b63b3c2250d4) (Video)
27. [Unique Factorization Domains 2](https://invisiblenetwork.ai/learn/nptel/111106131/68eef1a7abde) (Video)
28. [Gauss Lemma](https://invisiblenetwork.ai/learn/nptel/111106131/465fe24ed825) (Video)
29. [Z\[X\] is a UFD](https://invisiblenetwork.ai/learn/nptel/111106131/2780da01715f) (Video)
30. [Eisenstein criterion and Problems 7](https://invisiblenetwork.ai/learn/nptel/111106131/fe37eb97b9eb) (Video)
31. [Problems 8](https://invisiblenetwork.ai/learn/nptel/111106131/506938123e2b) (Video)
32. [Problems 9](https://invisiblenetwork.ai/learn/nptel/111106131/73ff42ed617e) (Video)
33. [Field extensions 1](https://invisiblenetwork.ai/learn/nptel/111106131/a4a04343761e) (Video)
34. [Field extensions 2](https://invisiblenetwork.ai/learn/nptel/111106131/78b800b63133) (Video)
35. [Degree of a field extension 1](https://invisiblenetwork.ai/learn/nptel/111106131/8d7130c60a3a) (Video)
36. [Degree of a field extension 2](https://invisiblenetwork.ai/learn/nptel/111106131/f859b58306df) (Video)
37. [Algebraic elements form a field](https://invisiblenetwork.ai/learn/nptel/111106131/a96a0e877ad6) (Video)
38. [Field homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106131/5c68e44cfb88) (Video)
39. [Splitting fields](https://invisiblenetwork.ai/learn/nptel/111106131/40e055123b17) (Video)
40. [Finite fields 1](https://invisiblenetwork.ai/learn/nptel/111106131/b848b67d3b39) (Video)
41. [Finite fields 2](https://invisiblenetwork.ai/learn/nptel/111106131/7bc3cdf445df) (Video)
42. [Finite fields 3](https://invisiblenetwork.ai/learn/nptel/111106131/1b8dcc7a991b) (Video)
43. [Problems 10](https://invisiblenetwork.ai/learn/nptel/111106131/c7bb0e3c584f) (Video)
44. [Problems 11](https://invisiblenetwork.ai/learn/nptel/111106131/8a7d8a210a0b) (Video)