# Introduction to Commutative Algebra

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Prof. A. V. Jayanthan
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106098)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106098)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Review of Ring Theory](https://invisiblenetwork.ai/learn/nptel/111106098/f900a065c13d) (Video)
2. [Review of Ring Theory (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/cc611e5c1b48) (Video)
3. [Ideals in commutative rings](https://invisiblenetwork.ai/learn/nptel/111106098/e8bb8af38edc) (Video)
4. [Operations on ideals](https://invisiblenetwork.ai/learn/nptel/111106098/6a47ee1ebdf6) (Video)
5. [Properties of prime ideals](https://invisiblenetwork.ai/learn/nptel/111106098/0f1b9124f97c) (Video)
6. [Colon and Radical of ideals](https://invisiblenetwork.ai/learn/nptel/111106098/a19791828732) (Video)
7. [Radicals, extension and contraction of ideals](https://invisiblenetwork.ai/learn/nptel/111106098/ab5353c63630) (Video)
8. [Modules and homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106098/58e4268ef317) (Video)
9. [Isomorphism theorems and Operations on modules](https://invisiblenetwork.ai/learn/nptel/111106098/3ec7118528b4) (Video)
10. [Operations on modules (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/9fd0629fa7c3) (Video)
11. [Module homomorphism and determinant trick](https://invisiblenetwork.ai/learn/nptel/111106098/ff3f59bc6b7a) (Video)
12. [Nakayama’s lemma and exact sequences](https://invisiblenetwork.ai/learn/nptel/111106098/b2db72cbae8a) (Video)
13. [Exact sequences (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/c06f6027bc81) (Video)
14. [Homomorphisms and Tensor products](https://invisiblenetwork.ai/learn/nptel/111106098/73941fe687e8) (Video)
15. [Properties of tensor products](https://invisiblenetwork.ai/learn/nptel/111106098/b028fc8d3ae8) (Video)
16. [Properties of tensor products (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/2481ca58e2d2) (Video)
17. [Tensor product of Algebras](https://invisiblenetwork.ai/learn/nptel/111106098/304b4961fc52) (Video)
18. [Localization](https://invisiblenetwork.ai/learn/nptel/111106098/7f34996306fc) (Video)
19. [Localization (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/e265659fcbb6) (Video)
20. [Local properties](https://invisiblenetwork.ai/learn/nptel/111106098/4f68c935a9a0) (Video)
21. [Further properties of localization](https://invisiblenetwork.ai/learn/nptel/111106098/884329eb38a5) (Video)
22. [Intergral dependence](https://invisiblenetwork.ai/learn/nptel/111106098/5f1a6ac2e0a0) (Video)
23. [Integral extensions](https://invisiblenetwork.ai/learn/nptel/111106098/de25a281541d) (Video)
24. [Lying over and Going-up theorems](https://invisiblenetwork.ai/learn/nptel/111106098/2043d0713d0d) (Video)
25. [Going-down theorem](https://invisiblenetwork.ai/learn/nptel/111106098/e09e380f2d17) (Video)
26. [Going-down theorem (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/84c30706ac30) (Video)
27. [Chain conditions](https://invisiblenetwork.ai/learn/nptel/111106098/c93f3e39d682) (Video)
28. [Noetherian and Artinian modules](https://invisiblenetwork.ai/learn/nptel/111106098/befb31304eb2) (Video)
29. [Properties of Noetherian and Artinian modules, Composition Series](https://invisiblenetwork.ai/learn/nptel/111106098/db10b310cb98) (Video)
30. [Further properties of Noetherian and Artinian modules and rings](https://invisiblenetwork.ai/learn/nptel/111106098/44d5d09c5bb4) (Video)
31. [Hilbert basis theorem and Primary decomposition](https://invisiblenetwork.ai/learn/nptel/111106098/4cd5f3c60410) (Video)
32. [Primary decomposition (Ctd.)](https://invisiblenetwork.ai/learn/nptel/111106098/31d1658d186b) (Video)
33. [Uniqueness of primary decomposition](https://invisiblenetwork.ai/learn/nptel/111106098/38fc3a4a5839) (Video)
34. [2nd Uniqueness theorem, Artinian rings](https://invisiblenetwork.ai/learn/nptel/111106098/084bf495c306) (Video)
35. [Properties of Artinian rings](https://invisiblenetwork.ai/learn/nptel/111106098/85fd1e93a10f) (Video)
36. [Structure Theorem of Artinian rings](https://invisiblenetwork.ai/learn/nptel/111106098/ed7afac1fa33) (Video)
37. [Noether Normalization](https://invisiblenetwork.ai/learn/nptel/111106098/02c65394ed38) (Video)
38. [Hilberts Nullstellensatz](https://invisiblenetwork.ai/learn/nptel/111106098/808f66da6da0) (Video)
39. [Live Session 02-03-2021](https://invisiblenetwork.ai/learn/nptel/111106098/f900a065c13d-2) (Video)