Last Updated
：2025/12/04
Galois extension
Noun
Japanese Meaning
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。
（ plural ）
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(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.
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Galois extension
When K is a Galois extension of F, every intermediate field corresponds to a subgroup of the Galois group Gal(K/F).
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When K is a Galois extension of F, every intermediate field corresponds to a subgroup of the Galois group Gal(K/F).
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