Galois extension
Algebraic field extension / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Galois extension?
Summarize this article for a 10 year old
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.[lower-alpha 1]
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]
The property of an extension being Galois behaves well with respect to field composition and intersection.[3]