# Computational Commutative Algebra

- Institution: Chennai Mathematical Institute
- Department: Mathematics
- Teacher: Prof. Manoj Kummini
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106138)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106138)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete proofs of theorems.

INTENDED AUDIENCE : Advanced undergraduate / post-graduate students

PREREQUISITES : Introduction to basic theory of rings, modules

## Lectures

1. [Definitions](https://invisiblenetwork.ai/learn/nptel/111106138/03a944175872) (YouTube)
2. [Homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106138/576b137af820) (YouTube)
3. [Quotient rings](https://invisiblenetwork.ai/learn/nptel/111106138/b585791cebdf) (YouTube)
4. [Noetherian rings](https://invisiblenetwork.ai/learn/nptel/111106138/eeceb97363d3) (YouTube)
5. [Monomials](https://invisiblenetwork.ai/learn/nptel/111106138/de7a38dd1e8d) (YouTube)
6. [Initial ideals](https://invisiblenetwork.ai/learn/nptel/111106138/a08c409e2c11) (YouTube)
7. [Division algorithm](https://invisiblenetwork.ai/learn/nptel/111106138/72fc000cbc85) (YouTube)
8. [Grobner basis](https://invisiblenetwork.ai/learn/nptel/111106138/5d58b8a7c88f) (YouTube)
9. [Solving Polynomial Equations](https://invisiblenetwork.ai/learn/nptel/111106138/db30ef22554a) (YouTube)
10. [Nullstellensatz - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/29a136a55a49) (YouTube)
11. [Nullstellensatz - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/e82c9ea04e82) (YouTube)
12. [Buchberger criterion](https://invisiblenetwork.ai/learn/nptel/111106138/c4d60e0d1675) (YouTube)
13. [Monomial basis](https://invisiblenetwork.ai/learn/nptel/111106138/d7463a8de641) (YouTube)
14. [Elimination](https://invisiblenetwork.ai/learn/nptel/111106138/80e79563931a) (YouTube)
15. [Modules - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/326b0533851a) (YouTube)
16. [Modules - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/c5748eb40fd2) (YouTube)
17. [Localisation](https://invisiblenetwork.ai/learn/nptel/111106138/6a0a7fbad8af) (YouTube)
18. [Nakayama Lemma](https://invisiblenetwork.ai/learn/nptel/111106138/c98d06882648) (YouTube)
19. [Spectrum - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/98676bf06e94) (YouTube)
20. [Spectrum - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/9d5adbd227c0) (YouTube)
21. [Associated primes](https://invisiblenetwork.ai/learn/nptel/111106138/6ffcaae9a8c9) (YouTube)
22. [Primary Decomposition](https://invisiblenetwork.ai/learn/nptel/111106138/1d10382abe67) (YouTube)
23. [Support of a module](https://invisiblenetwork.ai/learn/nptel/111106138/0a71ae97058d) (YouTube)
24. [Associated primes](https://invisiblenetwork.ai/learn/nptel/111106138/01a0cc9ac568) (YouTube)
25. [Prime avoidance](https://invisiblenetwork.ai/learn/nptel/111106138/fd946d3ccc4c) (YouTube)
26. [Saturation - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/cdd79d32ae8e) (YouTube)
27. [saturation - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/789fa7f8d35b) (YouTube)
28. [saturation - Part 3](https://invisiblenetwork.ai/learn/nptel/111106138/6631239f793f) (YouTube)
29. [Morphisms - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/85e2d67619a3) (YouTube)
30. [Morphisms - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/30c7b58c05cd) (YouTube)
31. [Integral extensions](https://invisiblenetwork.ai/learn/nptel/111106138/39d2cbb5dc16) (YouTube)
32. [Noether normalisation lemma](https://invisiblenetwork.ai/learn/nptel/111106138/4a04b708e98d) (YouTube)
33. [Noether normalisation lemma](https://invisiblenetwork.ai/learn/nptel/111106138/03d8bb5083ec) (YouTube)
34. [Polynomial rings](https://invisiblenetwork.ai/learn/nptel/111106138/97d1956e8cf6) (YouTube)
35. [Going up theorem](https://invisiblenetwork.ai/learn/nptel/111106138/36e887733c1b) (YouTube)
36. [Artinian rings](https://invisiblenetwork.ai/learn/nptel/111106138/3468c3761ada) (YouTube)
37. [Graded modules](https://invisiblenetwork.ai/learn/nptel/111106138/2983a26ce9d7) (YouTube)
38. [Hilbert polynomial](https://invisiblenetwork.ai/learn/nptel/111106138/088376c8f20b) (YouTube)
39. [Hilbert-Samuel polynomial](https://invisiblenetwork.ai/learn/nptel/111106138/41826e060da6) (YouTube)
40. [Artin Rees Lemma](https://invisiblenetwork.ai/learn/nptel/111106138/ebdb28b2ddec) (YouTube)
41. [Degree of Hilbert-Samuel polynomial](https://invisiblenetwork.ai/learn/nptel/111106138/9c3ff68bc926) (YouTube)
42. [Dimension of noetherian local rings - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/7ef60a9e1237) (YouTube)
43. [Dimension of noetherian local rings - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/f76fa36245f1) (YouTube)
44. [Dimension of polynomial rings](https://invisiblenetwork.ai/learn/nptel/111106138/ab6ff72a664e) (YouTube)
45. [Algebras over a field](https://invisiblenetwork.ai/learn/nptel/111106138/f148099aee8a) (YouTube)
46. [Graded rings - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/8e9747ecb53b) (YouTube)
47. [Graded rings - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/b9eeffbe1f88) (YouTube)
48. [Polynomial rings over fields](https://invisiblenetwork.ai/learn/nptel/111106138/4127d353d65f) (YouTube)
49. [Hilbert series - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/6c85984b40d1) (YouTube)
50. [Hilbert series - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/b55acc3ddeb9) (YouTube)
51. [Proj of a graded ring](https://invisiblenetwork.ai/learn/nptel/111106138/f6ef0f1e87ad) (YouTube)
52. [Homogenization - Part 1](https://invisiblenetwork.ai/learn/nptel/111106138/ba3b7724b716) (YouTube)
53. [Homogenization - Part 2](https://invisiblenetwork.ai/learn/nptel/111106138/c21963529568) (YouTube)
54. [More on graded rings](https://invisiblenetwork.ai/learn/nptel/111106138/33c8d9157e38) (YouTube)
55. [Free resolutions](https://invisiblenetwork.ai/learn/nptel/111106138/154b5d80a5b1) (YouTube)
56. [Computing syzygies](https://invisiblenetwork.ai/learn/nptel/111106138/5be8486b7f6a) (YouTube)
57. [Koszul complex](https://invisiblenetwork.ai/learn/nptel/111106138/fde1cad10857) (YouTube)
58. [More on Koszul complexes](https://invisiblenetwork.ai/learn/nptel/111106138/4d617f457a7f) (YouTube)
59. [Castelnuovo Mumford regularity](https://invisiblenetwork.ai/learn/nptel/111106138/fab0ec916598) (YouTube)
60. [Castelnuovo Mumford regularity](https://invisiblenetwork.ai/learn/nptel/111106138/755be7e48271) (YouTube)