English Dictionary

Galois extension

noun

(algebra, Galois theory) 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.

A Galois extension is a field extension that is also a Galois extension.

意味（1）

(algebra, Galois theory) 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.