# Commutative Algebra

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. Dilip Patil
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101116)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101116)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : Zariski Topology and K-Spectrum](https://invisiblenetwork.ai/learn/nptel/111101116/894bce2ce1c9) (Video)
2. [Lecture 2 : Algebraic Varieties and Classical Nullstelensatz](https://invisiblenetwork.ai/learn/nptel/111101116/576b02e1477b) (Video)
3. [Lecture 3 : Motivation for Krulls Dimension](https://invisiblenetwork.ai/learn/nptel/111101116/78f992387bfd) (Video)
4. [Lecture 4 : Chevalleys dimension](https://invisiblenetwork.ai/learn/nptel/111101116/a2566ca61181) (Video)
5. [Lecture 5 : Associated Prime Ideals of a Module](https://invisiblenetwork.ai/learn/nptel/111101116/dec9ca9f6bb8) (Video)
6. [Lecture 6 : Support of a Module](https://invisiblenetwork.ai/learn/nptel/111101116/40f1a4031bc7) (Video)
7. [Lecture 7 : Primary Decomposition](https://invisiblenetwork.ai/learn/nptel/111101116/2f170241aeee) (Video)
8. [Lecture 8 : Primary Decomposition(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/24693602d5b1) (Video)
9. [Lecture 9 : Uniqueness of Primary Decomposition](https://invisiblenetwork.ai/learn/nptel/111101116/93cfce14fdae) (Video)
10. [Lecture 10 : Modules of Finite Length](https://invisiblenetwork.ai/learn/nptel/111101116/d3b7edc0fa43) (Video)
11. [Lecture 11 : Modules of Finite Length(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/895e6e38289d) (Video)
12. [Lecture 12 : Introduction to Krull's Dimension](https://invisiblenetwork.ai/learn/nptel/111101116/188ffc98dd87) (Video)
13. [Lecture 13 : Noether Normalization Lemma(Classical Version)](https://invisiblenetwork.ai/learn/nptel/111101116/4773985f4897) (Video)
14. [Lecture 14 : Consequences of Noether Normalization Lemma](https://invisiblenetwork.ai/learn/nptel/111101116/cf3a18531cd9) (Video)
15. [Lecture 15 : Nil Radical and Jacobson Radical of Finite type Algebras over a Field and digression of Integral Extension](https://invisiblenetwork.ai/learn/nptel/111101116/43a398dbd2c6) (Video)
16. [Lecture 16 : Nagata's version of NNL](https://invisiblenetwork.ai/learn/nptel/111101116/14dea9439790) (Video)
17. [Lecture 17 : Dimensions of Polynomial ring over Noetherian rings](https://invisiblenetwork.ai/learn/nptel/111101116/7735360f05e6) (Video)
18. [Lecture 18 : Dimension of Polynomial Algebra over arbitrary Rings](https://invisiblenetwork.ai/learn/nptel/111101116/696e5fa8b24c) (Video)
19. [Lecture 19 : Dimension Inequalities](https://invisiblenetwork.ai/learn/nptel/111101116/c618998b75ad) (Video)
20. [Lecture 20 : Hilbert's Nullstelensatz](https://invisiblenetwork.ai/learn/nptel/111101116/fcbf8ca1a481) (Video)
21. [Lecture 21 : Computational rules for Poincaré Series](https://invisiblenetwork.ai/learn/nptel/111101116/9d1d3a4fbf52) (Video)
22. [Lecture 22 : Graded Rings, Modules and Poincaré Series](https://invisiblenetwork.ai/learn/nptel/111101116/93482363350a) (Video)
23. [Lecture 23 : Hilbert-Samuel Polynomials](https://invisiblenetwork.ai/learn/nptel/111101116/5e9e8002e01c) (Video)
24. [Lecture 24 : Hilbert-Samuel Polynomials(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/df59a806add2) (Video)
25. [Lecture 25 : Numerical Function of polynomial type](https://invisiblenetwork.ai/learn/nptel/111101116/428433a9f667) (Video)
26. [Lecture 26 : Hilbert-Samuel Polynomial of a Local ring](https://invisiblenetwork.ai/learn/nptel/111101116/671aeb1cf268) (Video)
27. [Lecture 27 : Filtration on a Module](https://invisiblenetwork.ai/learn/nptel/111101116/23edb651d041) (Video)
28. [Lecture 28 : Artin-Rees Lemma](https://invisiblenetwork.ai/learn/nptel/111101116/770c38667555) (Video)
29. [Lecture 29 : Dimension Theorem](https://invisiblenetwork.ai/learn/nptel/111101116/be18194fb048) (Video)
30. [Lecture 30 : Dimension Theorem(Continued)](https://invisiblenetwork.ai/learn/nptel/111101116/22f323ca462e) (Video)
31. [Lecture 31 : Consequences of Dimension Theorem](https://invisiblenetwork.ai/learn/nptel/111101116/e90b75cb46c2) (Video)
32. [Lecture 32 : Generalized Krull's Principal Ideal Theorem](https://invisiblenetwork.ai/learn/nptel/111101116/2f1d2cb8445f) (Video)
33. [Lecture 33 : Second proof of Krull's Principal Ideal Theorem](https://invisiblenetwork.ai/learn/nptel/111101116/a448abe78ddf) (Video)
34. [Lecture 34 : The Spec Functor](https://invisiblenetwork.ai/learn/nptel/111101116/93576b9aa62a) (Video)
35. [Lecture 35 : Prime ideals in Polynomial rings](https://invisiblenetwork.ai/learn/nptel/111101116/750988d3ccb5) (Video)
36. [Lecture 36 : Characterization of Equidimensional Affine Algebra](https://invisiblenetwork.ai/learn/nptel/111101116/86c6f5bf461c) (Video)
37. [Lecture 37 : Connection between Regular local rings and associated graded rings](https://invisiblenetwork.ai/learn/nptel/111101116/395e8aa1786e) (Video)
38. [Lecture 38 : Statement of the Jacobian Criterion for Regularity](https://invisiblenetwork.ai/learn/nptel/111101116/2726429f40e6) (Video)
39. [Lecture 39 : Hilbert function for Affine Algebra](https://invisiblenetwork.ai/learn/nptel/111101116/ad12dccd8068) (Video)
40. [Lecture 40 : Hilbert Serre Theorem](https://invisiblenetwork.ai/learn/nptel/111101116/d73aeee46675) (Video)
41. [Lecture 41 : Jacobian Matrix and its Rank](https://invisiblenetwork.ai/learn/nptel/111101116/0f01cbad143c) (Video)
42. [Lecture 42 : Jacobian Matrix and its Rank(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/4a19315cc69f) (Video)
43. [Lecture 43 : Proof of Jacobian Critrerion](https://invisiblenetwork.ai/learn/nptel/111101116/c8e05acccbe1) (Video)
44. [Lecture 44 : Proof of Jacobian Critrerion(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/27c5d4f1a654) (Video)
45. [Lecture 45 : Preparation for Homological Dimension](https://invisiblenetwork.ai/learn/nptel/111101116/c3ddc5eaaa5d) (Video)
46. [Lecture 46 : Complexes of Modules and Homology](https://invisiblenetwork.ai/learn/nptel/111101116/a578d62deddc) (Video)
47. [Lecture 47 : Projective Modules](https://invisiblenetwork.ai/learn/nptel/111101116/a9018407d183) (Video)
48. [Lecture 48 : Homological Dimension and Projective module](https://invisiblenetwork.ai/learn/nptel/111101116/bd36b7344a78) (Video)
49. [Lecture 49 : Global Dimension](https://invisiblenetwork.ai/learn/nptel/111101116/70a24b3eb216) (Video)
50. [Lecture 50 : Homological characterization of Regular Local Ring(RLR)](https://invisiblenetwork.ai/learn/nptel/111101116/302889a6c65c) (Video)
51. [Lecture 51 : Homological characterization of Regular Local Ring(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/9bba747c5030) (Video)
52. [Lecture 52 : Homological Characterization of Regular Local Rings(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/a84be2ce9a9d) (Video)
53. [Lecture 53 : Regular Local Rings are UFD](https://invisiblenetwork.ai/learn/nptel/111101116/cc468bf5b2f3) (Video)
54. [Lecture 54 : RLR-Prime ideals of height 1](https://invisiblenetwork.ai/learn/nptel/111101116/477a1984b324) (Video)
55. [Lecture 55 : Discrete Valuation Ring](https://invisiblenetwork.ai/learn/nptel/111101116/42d33b6ab4aa) (Video)
56. [Lecture 56 : Discrete Valuation Ring(Contd)](https://invisiblenetwork.ai/learn/nptel/111101116/7c9242d050f8) (Video)
57. [Lecture 57 : Dedekind Domains](https://invisiblenetwork.ai/learn/nptel/111101116/5909a3365fa6) (Video)
58. [Lecture 58 : Fractionary Ideals and Dedekind Domains](https://invisiblenetwork.ai/learn/nptel/111101116/f6df6ac99dff) (Video)
59. [Lecture 59 : Characterization of Dedekind Domain](https://invisiblenetwork.ai/learn/nptel/111101116/69d7397b5432) (Video)
60. [Lecture 60 : Dedekind Domains and prime factorization of ideals](https://invisiblenetwork.ai/learn/nptel/111101116/af1bcaabdaf7) (Video)