Learn · Introduction to Galois Theory
Lecture 20 of 49Week 4
Characterization of Galois extensions - Part 1
Prof. Krishna Hanumanthu · Chennai Mathematical Institute
Credits and licence
- From
- Introduction to Galois Theory, Chennai Mathematical Institute (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures
- Motivation and overview of the course
- Review of group theory
- Review of ring theory I
- Review of ring theory II
- Review of field theory I
- Review of field theory II
- Review of field theory III
- Problem Session 1
- Problem Session 2
- Beginning of Galois theory
- Fixed fields
- Theorem I on fixed fields
- Theorem II on fixed fields
- Galois extensions, Galois groups
- Normal extensions
- Problem Session - Part 3
- Problem Session - Part 4
- Separable extension - Part 1
- Separable extension - Part 2
- Characterization of Galois extensions - Part 1
- Characterization of Galois extensions - Part 2
- Examples of Galois extensions
- Motivating the main theorem of Galois theory
- Main theorem of Galois theory - Part 1
- Main theorem of Galois theory - Part 2
- Fundamental theorem of algebra
- Problem Session - Part 5
- Problem Session - Part 6
- Problem Session - Part 7
- Problem Session - Part 8
- Problem Session - Part 9
- Kummer extensions - Part 1
- Kummer extensions - Part 2
- Kummer extensions - Part 3
- Cyclotomic extensions - Part 1
- Cyclotomic extensions - Part 2
- Solvability by radicals
- Characterizations of solvability - Part 1
- Characterizations of solvability - Part 2
- Discriminants, Galois groups of polynomials
- Quartics are solvable
- Solvable groups - Part 1
- Solvable groups - Part 2
- Solvable groups - Part 3
- Insolvability of quintics
- Problem Session - Part 10
- Problem Session - Part 11
- Problem Session - Part 12
- Problem Session - Part 13