normal algebraic extension

正规扩张

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

Translation evidence: Literature usage

Meaning in context

An algebraic extension $L/K$ such that every irreducible polynomial over $K$ having a root in $L$ splits completely in $L$.

基域上的不可约多项式一旦在扩域中有根，就在其中完全分裂的代数扩张。

Example

$\mathbb F_p(t^{1/p})/\mathbb F_p(t)$ is normal but inseparable.

Usage and distinctions

Normality does not imply separability or perfectness of either field.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source分裂域和正规扩张 (sec:splitting-field), definition-theorem def:normal-ext, condition N.1 and sentence naming 正规扩张 · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件分裂域和正规扩张 (sec:splitting-field), definition-theorem def:normal-ext, condition N.1 and sentence naming 正规扩张 · Checked 2026-10-15

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