Galois extension

Galois 扩张

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

An algebraic field extension that is both normal and separable.

同时正规且可分的代数域扩张。

Example

Q(2)/Q\mathbb Q(\sqrt2)/\mathbb Q is Galois.

Usage and distinctions

For a finite extension its automorphism group has size equal to the degree exactly in this case.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source有限 Galois 对应, definition def:Galois-ext, 可分正规扩张 clause (no finiteness restriction in this definition) · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件有限 Galois 对应, definition def:Galois-ext, 可分正规扩张 clause (no finiteness restriction in this definition) · Checked 2026-10-15
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