# Category:Galois theory

Here is a list of articles in the Galois theory category of the Computing portal that unifies foundations of mathematics and computations using computers.

In mathematics, **Galois theory** is a branch of abstract algebra.

At the most basic level, it uses permutation groups to describe how the various roots of a given polynomial equation are related to each other. This was the original point of view of Évariste Galois.

The modern approach to Galois theory, developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others, involves studying automorphisms of field extensions.

## Pages in category "Galois theory"

The following 40 pages are in this category, out of 40 total.

- Galois theory
*(computing)*

### A

- Abel–Ruffini theorem
*(computing)* - Abhyankar's conjecture
*(computing)* - Absolute Galois group
*(computing)* - Artin–Schreier theory
*(computing)*

### B

- Biquadratic field
*(computing)*

### E

- Elkies trinomial curves
*(computing)* - Embedding problem
*(computing)*

### F

- Field arithmetic
*(computing)* - Fontaine's period rings
*(computing)* - Fontaine–Mazur conjecture
*(computing)* - Frobenius endomorphism
*(computing)* - Fundamental theorem of Galois theory
*(computing)*

### G

- Galois cohomology
*(computing)* - Galois connection
*(computing)* - Galois extension
*(computing)* - Galois group
*(computing)* - Galois module
*(computing)* - Gaussian period
*(computing)* - Generic polynomial
*(computing)* - Grothendieck–Katz p-curvature conjecture
*(computing)*

### H

- Haran's diamond theorem
*(computing)* - Hasse–Arf theorem
*(computing)*

### I

- Inverse Galois problem
*(computing)*

### L

- Local Euler characteristic formula
*(computing)* - Local Tate duality
*(computing)*

### N

- Newton's identities
*(computing)*

### O

- Octic equation
*(computing)*

### P

- P-adic Hodge theory
*(computing)*

### Q

- Quintic function
*(computing)*

### R

- Radical extension
*(computing)* - Ramification theory of valuations
*(computing)* - Resolvent (Galois theory)
*(computing)*

### S

- Septic equation
*(computing)* - Sextic equation
*(computing)* - Shafarevich's theorem on solvable Galois groups
*(computing)* - Splitting of prime ideals in Galois extensions
*(computing)*

### T

- Tate duality
*(computing)* - Topological Galois theory
*(computing)*

### W

- Wiles's proof of Fermat's Last Theorem
*(computing)*