number field

数域

Number Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: algebraic number field

Translation evidence: Literature usage

Meaning in context

A field $K$ containing $\mathbb Q$ with finite degree $[K:\mathbb Q]$.

有理数域 $\mathbb Q$ 的有限扩张。

Example

$\mathbb Q(\sqrt2)$ has degree $2$ over $\mathbb Q$.

Usage and distinctions

$\mathbb Q(t)$ with transcendental $t$ is not a number field; algebraicity alone without finite degree also does not suffice.

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Definition sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义Chapter 1 opening paragraph, printed page 1: finite extension of Q · Checked 2026-10-14

Translation sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义第一章开头，printed page 1 代数数域 · Checked 2026-10-14

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