# Galois extension

In mathematics, a **Galois extension** is an algebraic field extension *E*/*F* that is normal and separable;^{[1]} or equivalently, *E*/*F* is algebraic, and the field fixed by the automorphism group Aut(*E*/*F*) is precisely the base field *F*. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory.^{[a]}

A result of Emil Artin allows one to construct Galois extensions as follows: If *E* is a given field, and *G* is a finite group of automorphisms of *E* with fixed field *F*, then *E*/*F* is a Galois extension.^{[2]}