# Algebra - II

- Institution: IMSc
- Department: Mathematics
- Teacher: Prof. Sankaran Viswanath Prof. Amritanshu Prasad
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106151)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106151)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Algebraic and Transcendental Numbers](https://invisiblenetwork.ai/learn/nptel/111106151/1b3aa18f717e) (Video)
2. [Extensions Generated by Elements](https://invisiblenetwork.ai/learn/nptel/111106151/7f1e55a63cbf) (Video)
3. [Isomorphic Extensions](https://invisiblenetwork.ai/learn/nptel/111106151/236579c8b786) (Video)
4. [Degree of an Extension](https://invisiblenetwork.ai/learn/nptel/111106151/5fd23d6198cf) (Video)
5. [Constructible Numbers](https://invisiblenetwork.ai/learn/nptel/111106151/5f7a8b5a276b) (Video)
6. [The Field of Constructible Numbers](https://invisiblenetwork.ai/learn/nptel/111106151/72b378ca06e4) (Video)
7. [Characterization of Constructible Numbers](https://invisiblenetwork.ai/learn/nptel/111106151/603f5d56e0ec) (Video)
8. [Solved Problems (Week 1)](https://invisiblenetwork.ai/learn/nptel/111106151/151524ebd67b) (Video)
9. [Some Things can't be Constructed](https://invisiblenetwork.ai/learn/nptel/111106151/134e35d76825) (Video)
10. [Symbolic Adjunction](https://invisiblenetwork.ai/learn/nptel/111106151/9ff8678270ba) (Video)
11. [Repeated Roots](https://invisiblenetwork.ai/learn/nptel/111106151/fb2419338fcf) (Video)
12. [Gauss Lemma](https://invisiblenetwork.ai/learn/nptel/111106151/ec97dddc882b) (Video)
13. [Eisenstein's criterion](https://invisiblenetwork.ai/learn/nptel/111106151/68e7f227d0f9) (Video)
14. [Existence Theorem for Finite Fields](https://invisiblenetwork.ai/learn/nptel/111106151/6cbe77e31110) (Video)
15. [Subfields of a Finite Field](https://invisiblenetwork.ai/learn/nptel/111106151/eb9aad0b5719) (Video)
16. [Multiplicative Group of a Finite Field](https://invisiblenetwork.ai/learn/nptel/111106151/3a20db2acad4) (Video)
17. [Uniqueness Theorem for Finite Fields](https://invisiblenetwork.ai/learn/nptel/111106151/8a00952695d0) (Video)
18. [Solved Problems (week 2)](https://invisiblenetwork.ai/learn/nptel/111106151/0977fb4cb9fb) (Video)
19. [Algebraic Extensions and Algebraic Closures](https://invisiblenetwork.ai/learn/nptel/111106151/c7f368704eac) (Video)
20. [Existence of Algebraic Closures](https://invisiblenetwork.ai/learn/nptel/111106151/437a20c20b43) (Video)
21. [Uniqueness of Algebraic Closure](https://invisiblenetwork.ai/learn/nptel/111106151/a61d40af7489) (Video)
22. [Solved Problems, part 1 (Week 3)](https://invisiblenetwork.ai/learn/nptel/111106151/f7dea9b90412) (Video)
23. [Existence of splitting fields, bound on degree](https://invisiblenetwork.ai/learn/nptel/111106151/74217060dcf2) (Video)
24. [Uniqueness of splitting fields](https://invisiblenetwork.ai/learn/nptel/111106151/cedd37ec0e6b) (Video)
25. [Solved problems , part 2 (Week 3)](https://invisiblenetwork.ai/learn/nptel/111106151/b0c994526b0a) (Video)
26. [Normal Extensions](https://invisiblenetwork.ai/learn/nptel/111106151/f1b4e5ce3876) (Video)
27. [Separable polynomials](https://invisiblenetwork.ai/learn/nptel/111106151/1509890d3d6b) (Video)
28. [Perfect fields, separable extensions](https://invisiblenetwork.ai/learn/nptel/111106151/7e3ddf43077b) (Video)
29. [Definition and examples, fixed fields](https://invisiblenetwork.ai/learn/nptel/111106151/0b9b3ada1272) (Video)
30. [Characterization of Galois extensions](https://invisiblenetwork.ai/learn/nptel/111106151/97fa3ab649ce) (Video)
31. [Linear Independence of Characters](https://invisiblenetwork.ai/learn/nptel/111106151/5ae73dd0dcb1) (Video)
32. [Solved problems (Week 4)](https://invisiblenetwork.ai/learn/nptel/111106151/d1f24665bc3f) (Video)
33. [Artin's Theorem - part 1](https://invisiblenetwork.ai/learn/nptel/111106151/46d5eab97948) (Video)
34. [Artin's Theorem - part 2](https://invisiblenetwork.ai/learn/nptel/111106151/07d4e6ccc2fc) (Video)
35. [Finite Galois Extensions](https://invisiblenetwork.ai/learn/nptel/111106151/c66313d5323e) (Video)
36. [The fundamental theorem of Galois Theory - 1](https://invisiblenetwork.ai/learn/nptel/111106151/03a92f099486) (Video)
37. [The fundamental theorem of Galois Theory - 2](https://invisiblenetwork.ai/learn/nptel/111106151/a2470beb5617) (Video)
38. [Solved problems (Week 5)](https://invisiblenetwork.ai/learn/nptel/111106151/588869028538) (Video)
39. [Cyclotomic extensions](https://invisiblenetwork.ai/learn/nptel/111106151/0738e3a3bb6e) (Video)
40. [Irreducibility of the cyclotomic polynomial](https://invisiblenetwork.ai/learn/nptel/111106151/fcd936d986d7) (Video)
41. [Application: Constructibility of regular n-gons.](https://invisiblenetwork.ai/learn/nptel/111106151/47517805e1eb) (Video)
42. [Insolvability of the general quintic - part 1](https://invisiblenetwork.ai/learn/nptel/111106151/6a2c91c33a2b) (Video)
43. [Insolvability of the general quintic - part 2](https://invisiblenetwork.ai/learn/nptel/111106151/428062c20ef1) (Video)
44. [Insolvability of the general quintic - part 3](https://invisiblenetwork.ai/learn/nptel/111106151/8d2aac695639) (Video)
45. [What is category theory (and why is it important)?](https://invisiblenetwork.ai/learn/nptel/111106151/68a4ddcb1029) (Video)
46. [Definition of a category](https://invisiblenetwork.ai/learn/nptel/111106151/d9e413f0cac5) (Video)
47. [Monomorphisms, epimorphisms, and isomorphisms](https://invisiblenetwork.ai/learn/nptel/111106151/e931bce68c4d) (Video)
48. [Categories: First Problem Session](https://invisiblenetwork.ai/learn/nptel/111106151/70931905451b) (Video)
49. [Initial and Terminal Objects](https://invisiblenetwork.ai/learn/nptel/111106151/d81bea07b2bf) (Video)
50. [Products and Coproducts](https://invisiblenetwork.ai/learn/nptel/111106151/0ec611b7d55e) (Video)
51. [Categories: Second Problem Session](https://invisiblenetwork.ai/learn/nptel/111106151/9169295bc140) (Video)
52. [Functors](https://invisiblenetwork.ai/learn/nptel/111106151/ce40ff0ed641) (Video)
53. [The Category of Categories](https://invisiblenetwork.ai/learn/nptel/111106151/47043f868133) (Video)
54. [Natural Transformations](https://invisiblenetwork.ai/learn/nptel/111106151/6887985f0dad) (Video)
55. [Functor Categories](https://invisiblenetwork.ai/learn/nptel/111106151/cb36e559db16) (Video)
56. [Categories: Third Problem Session](https://invisiblenetwork.ai/learn/nptel/111106151/8eb75ed7d4c1) (Video)
57. [Adjunction](https://invisiblenetwork.ai/learn/nptel/111106151/8a5ec1f8f45d) (Video)
58. [Categories: Fourth Problem Session](https://invisiblenetwork.ai/learn/nptel/111106151/01e1bcf58d81) (Video)
59. [Tensor products of Z-modules](https://invisiblenetwork.ai/learn/nptel/111106151/0a91180b94a6) (Video)
60. [Free abelian groups and quotient groups](https://invisiblenetwork.ai/learn/nptel/111106151/f84aab2bc162) (Video)
61. [Construction of the tensor product](https://invisiblenetwork.ai/learn/nptel/111106151/c6cebe10538d) (Video)
62. [Problem session](https://invisiblenetwork.ai/learn/nptel/111106151/d6efaaf144b0) (Video)
63. [Tensor product of R-modules](https://invisiblenetwork.ai/learn/nptel/111106151/27bc9cc7caed) (Video)
64. [Functoriality of the tensor product](https://invisiblenetwork.ai/learn/nptel/111106151/101964bfe0ab) (Video)
65. [Bimodules](https://invisiblenetwork.ai/learn/nptel/111106151/0515d7c4a4df) (Video)
66. [Tensor products of bimodules](https://invisiblenetwork.ai/learn/nptel/111106151/00d310956ad6) (Video)
67. [Tensor products of modules over commutative rings](https://invisiblenetwork.ai/learn/nptel/111106151/fa343c485182) (Video)
68. [Extension of scalars](https://invisiblenetwork.ai/learn/nptel/111106151/f675431156c7) (Video)
69. [Problem session - tensor products of vector spaces](https://invisiblenetwork.ai/learn/nptel/111106151/550cd00c5775) (Video)
70. [Some Properties of the tensor product](https://invisiblenetwork.ai/learn/nptel/111106151/9ea2e581ac1d) (Video)
71. [F-algebras](https://invisiblenetwork.ai/learn/nptel/111106151/ddfc76ae352c) (Video)
72. [Composition Series](https://invisiblenetwork.ai/learn/nptel/111106151/9710c40c1e96) (Video)
73. [Schreier's Theorem](https://invisiblenetwork.ai/learn/nptel/111106151/b512da914a36) (Video)
74. [Ascending and Descending Chain Conditions](https://invisiblenetwork.ai/learn/nptel/111106151/9da4ee5f63a4) (Video)
75. [Existence of Jordan-Holder Series](https://invisiblenetwork.ai/learn/nptel/111106151/538e3ad88917) (Video)
76. [The Jordan-Holder Theorem](https://invisiblenetwork.ai/learn/nptel/111106151/912151832e21) (Video)
77. [Examples related to the Jordan-Holder Theorem](https://invisiblenetwork.ai/learn/nptel/111106151/3a64a0f865c3) (Video)
78. [The Jordan-Holder Theorem for Groups](https://invisiblenetwork.ai/learn/nptel/111106151/68edf5b17e3d) (Video)
79. [Indecomposable Modules](https://invisiblenetwork.ai/learn/nptel/111106151/679e95ae5e97) (Video)
80. [Direct Sum Decompositions](https://invisiblenetwork.ai/learn/nptel/111106151/cb5a05655709) (Video)
81. [Decomposition as a sum of Indecomposables](https://invisiblenetwork.ai/learn/nptel/111106151/e242f91a20c8) (Video)
82. [The Endomorphism Ring of an Indecomposable Module](https://invisiblenetwork.ai/learn/nptel/111106151/6b71d9de72da) (Video)
83. [Krull-Schmidt Theorem](https://invisiblenetwork.ai/learn/nptel/111106151/04a553c3815d) (Video)
84. [Krull-Schmidt Examples](https://invisiblenetwork.ai/learn/nptel/111106151/9079204ceb9f) (Video)
85. [Live Session 05-03-2021](https://invisiblenetwork.ai/learn/nptel/111106151/1b3aa18f717e-2) (Video)
86. [Live Session 03-04-2021](https://invisiblenetwork.ai/learn/nptel/111106151/7f1e55a63cbf-2) (Video)