Galois extension

noun1

1. •
   An algebraic extension that is both a normal and a separable extension; equivalently, an algebraic extension E/F such that the fixed field of its automorphism group (Galois group) Aut(E/F) is the base field F.

   • The significance of a Galois extension is that it has a Galois group and obeys the fundamental theorem of Galois theory.
   • The fundamental theorem of Galois theory states that there is a one-to-one correspondence between the subfields of a Galois extension and the subgroups of its Galois group.