field extension

域扩张

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

Translation evidence: Literature usage

Meaning in context

A field LL together with an injective unital field homomorphism K→LK\to L, usually identified with a subfield inclusion.

一个域及一个基域到它的含幺嵌入，通常把基域看成其子域。

Example

Q⊂Q(2)\mathbb Q\subset\mathbb Q(\sqrt2) has degree two.

Usage and distinctions

The degree is vector-space dimension, not the number of field elements.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source扩张的几种类型, opening paragraph defining 域扩张 as an embedding F→E and identifying F with a subfield · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件扩张的几种类型, opening paragraph defining 域扩张 as an embedding F→E and identifying F with a subfield · Checked 2026-10-15
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