nLab
Galois extension

Classically, “Galois extension” refers to a class of extensions of fields.

An extension KLK\subset L of fields is Galois if it is normal and separable. In that case, the automorphism group Aut K(L)Aut_K(L) of KK-automorphisms of LL is called the Galois group and often denoted by Gal(L:K)Gal(L:K).

There is a famous Galois theory for such extensions.

Now there are numerous generalizations, including Hopf-Galois extensions, coalgebra Galois extensions etc.

Revised on February 5, 2010 20:44:24 by Toby Bartels (173.60.119.197)