English Dictionary

Galois extension

名詞

(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.

日本語の意味

ガロア拡大とは、正規かつ分離可能な代数拡大のことです。すなわち、ある体 F の上の代数拡大 E に対して、その自己同型群（ガロア群）の固定体が F に一致する場合、この拡大をガロア拡大と呼びます。

When K is a Galois extension of F, every intermediate field corresponds to a subgroup of the Galois group Gal(K/F).

K が F の正規かつ分離的な代数拡大であるとき、すべての中間体はガロア群 Gal(K/F) の部分群に対応する。

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.

Galois extensions （ plural ）