# Introduction to Algebraic Geometry and Commutative Algebra

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. Dilip P. Patil
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108136)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108136)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Motivation for K-algebraic sets](https://invisiblenetwork.ai/learn/nptel/111108136/04c6a27d7103) (Video)
2. [Definitions and examples of Affine Algebraic Set](https://invisiblenetwork.ai/learn/nptel/111108136/730ac8f846a5) (Video)
3. [Rings and Ideals](https://invisiblenetwork.ai/learn/nptel/111108136/baf6c101b18a) (Video)
4. [Operation on Ideals](https://invisiblenetwork.ai/learn/nptel/111108136/3989c96e3881) (Video)
5. [Prime Ideals and Maximal Ideals](https://invisiblenetwork.ai/learn/nptel/111108136/7a6613ed5d3c) (Video)
6. [Krull's Theorem and consequences](https://invisiblenetwork.ai/learn/nptel/111108136/9d723a529ea6) (Video)
7. [Module, submodules and quotient modules](https://invisiblenetwork.ai/learn/nptel/111108136/787ce83df802) (Video)
8. [Algebras and polynomial algebras](https://invisiblenetwork.ai/learn/nptel/111108136/7a5325483c5e) (Video)
9. [Universal property of polynomial algebra and examples](https://invisiblenetwork.ai/learn/nptel/111108136/39d904eb5eaa) (Video)
10. [Finite and Finite type algebras](https://invisiblenetwork.ai/learn/nptel/111108136/1e7ce7adceba) (Video)
11. [K-Spectrum (K-rational points)](https://invisiblenetwork.ai/learn/nptel/111108136/649bee752d44) (Video)
12. [Identity theorem for Polynomial functions](https://invisiblenetwork.ai/learn/nptel/111108136/497fc015b83d) (Video)
13. [Basic properties of K-algebraic sets](https://invisiblenetwork.ai/learn/nptel/111108136/9b07da35c24f) (Video)
14. [Examples of K-algebraic sets](https://invisiblenetwork.ai/learn/nptel/111108136/a4be917f6670) (Video)
15. [K-Zariski Topology](https://invisiblenetwork.ai/learn/nptel/111108136/813e4b508b35) (Video)
16. [The map V L](https://invisiblenetwork.ai/learn/nptel/111108136/013f8faa7f86) (Video)
17. [Noetherian and Artinian Ordered sets](https://invisiblenetwork.ai/learn/nptel/111108136/d3005f257186) (Video)
18. [Noetherian induction and Transfinite induction](https://invisiblenetwork.ai/learn/nptel/111108136/2b27e8a5b9ff) (Video)
19. [Modules with Chain Conditions](https://invisiblenetwork.ai/learn/nptel/111108136/d55f947cec8c) (Video)
20. [Properties of Noetherian and Artinian Modules](https://invisiblenetwork.ai/learn/nptel/111108136/45394f60cf01) (Video)
21. [Examples of Artinian and Noetherian Modules](https://invisiblenetwork.ai/learn/nptel/111108136/e296932505bf) (Video)
22. [Finite modules over Noetherian Rings](https://invisiblenetwork.ai/learn/nptel/111108136/cbefcf2147e3) (Video)
23. [Hilbert's Basis Theorem(HBT)](https://invisiblenetwork.ai/learn/nptel/111108136/19ca65294b8b) (Video)
24. [Consequences of HBT](https://invisiblenetwork.ai/learn/nptel/111108136/42983a31ca78) (Video)
25. [Free Modules and rank](https://invisiblenetwork.ai/learn/nptel/111108136/2b29523292f3) (Video)
26. [More on Noetherian and Artinian modules](https://invisiblenetwork.ai/learn/nptel/111108136/93f8d3d5ce7a) (Video)
27. [Ring of Fractions(Localization)](https://invisiblenetwork.ai/learn/nptel/111108136/4092890657de) (Video)
28. [Nil radical, contraction of ideals](https://invisiblenetwork.ai/learn/nptel/111108136/a37c318a6c61) (Video)
29. [Universal property of S -1 A](https://invisiblenetwork.ai/learn/nptel/111108136/15da010c87f7) (Video)
30. [Ideal structure in S -1 A](https://invisiblenetwork.ai/learn/nptel/111108136/3948b9652d40) (Video)
31. [Consequences of the Correspondence of Ideals](https://invisiblenetwork.ai/learn/nptel/111108136/4ab04dd14d07) (Video)
32. [Consequences of the Correspondence of Ideals(Contd.)](https://invisiblenetwork.ai/learn/nptel/111108136/f69bbb28d6d1) (Video)
33. [Modules of Fraction and universal properties](https://invisiblenetwork.ai/learn/nptel/111108136/8e027dd754d6) (Video)
34. [Exactness of the functor S -1](https://invisiblenetwork.ai/learn/nptel/111108136/3445cb82fafb) (Video)
35. [Universal property of Modules of Fractions](https://invisiblenetwork.ai/learn/nptel/111108136/4d6d84f00dd8) (Video)
36. [Further properties of Modules and Module of Fractions](https://invisiblenetwork.ai/learn/nptel/111108136/a986bc2025a5) (Video)
37. [Local-Global Principle](https://invisiblenetwork.ai/learn/nptel/111108136/fe1e800096d9) (Video)
38. [Consequences of Local-Global Principle](https://invisiblenetwork.ai/learn/nptel/111108136/906a5598ea6e) (Video)
39. [Properties of Artinian Rings](https://invisiblenetwork.ai/learn/nptel/111108136/488f42dfc8a1) (Video)
40. [Krull-Nakayama Lemma](https://invisiblenetwork.ai/learn/nptel/111108136/5333c04a1588) (Video)
41. [Properties of I K and V L maps](https://invisiblenetwork.ai/learn/nptel/111108136/891b22946775) (Video)
42. [Hilbert's Nullstelensatz](https://invisiblenetwork.ai/learn/nptel/111108136/fcaaed4f02a0) (Video)
43. [Hilbert's Nullstelensatz(Contd.)](https://invisiblenetwork.ai/learn/nptel/111108136/38d5b9765f30) (Video)
44. [Proof of Zariski's Lemma(HNS 3)](https://invisiblenetwork.ai/learn/nptel/111108136/f34b25e562bd) (Video)
45. [Consequences of HNS](https://invisiblenetwork.ai/learn/nptel/111108136/b5d3e43d90f9) (Video)
46. [Consequences of HNS(Contd.)](https://invisiblenetwork.ai/learn/nptel/111108136/5a23dd27e790) (Video)
47. [Jacobson Ring and examples](https://invisiblenetwork.ai/learn/nptel/111108136/80d4c4822f0e) (Video)
48. [Irreducible subsets of Zariski Topology(Finite type K-algebra)](https://invisiblenetwork.ai/learn/nptel/111108136/50fb049546f8) (Video)
49. [Spec functor on Finite type K-algebras](https://invisiblenetwork.ai/learn/nptel/111108136/9f02b0f52b2e) (Video)
50. [Properties of Irreducible topological spaces](https://invisiblenetwork.ai/learn/nptel/111108136/078e5dae012a) (Video)
51. [Zariski Topology on arbitrary commutative rings](https://invisiblenetwork.ai/learn/nptel/111108136/d88b273c599a) (Video)
52. [Spec functor on arbitrary commutative rings](https://invisiblenetwork.ai/learn/nptel/111108136/2852284b6b77) (Video)
53. [Topological properties of Spec A](https://invisiblenetwork.ai/learn/nptel/111108136/140d750cf1ee) (Video)
54. [Example to support the term Spectrum-](https://invisiblenetwork.ai/learn/nptel/111108136/6ab81eadc4e8) (Video)
55. [Integral Extensions](https://invisiblenetwork.ai/learn/nptel/111108136/327f5ad678d6) (Video)
56. [Elementwise characterization of Integral extensions](https://invisiblenetwork.ai/learn/nptel/111108136/f77ea7d30eff) (Video)
57. [Properties and examples of Integral extensions](https://invisiblenetwork.ai/learn/nptel/111108136/21599c185e43) (Video)
58. [Prime and Maximal ideals in integral extensions](https://invisiblenetwork.ai/learn/nptel/111108136/460ef1063c73) (Video)
59. [Lying over Theorem](https://invisiblenetwork.ai/learn/nptel/111108136/fa76a6374c08) (Video)
60. [Cohen-Siedelberg Theorem](https://invisiblenetwork.ai/learn/nptel/111108136/0fad27af0d48) (Video)
61. [Live Session 17-03-2022](https://invisiblenetwork.ai/learn/nptel/111108136/04c6a27d7103-2) (Video)
62. [Live Session 03-03-2025](https://invisiblenetwork.ai/learn/nptel/111108136/730ac8f846a5-2) (Video)