Galois theory

Galois theory is a branch of abstract algebra that studies the relationships between field extensions and group theory, particularly focusing on the solvability of polynomial equations. Named after the mathematician Évariste Galois, it provides a powerful framework for understanding how the roots of polynomials are related to the symmetry properties of the equations. The core ideas of Galois theory can be summarized as follows: 1. **Field Extensions**: A field extension is a bigger field that contains a smaller field.