integral basis of a number field

数域的整基

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

Translation evidence: Literature usage

Meaning in context

A $\mathbb Z$-basis of the additive group $\mathcal O_K$ for a number field $K$.

数域整数环 $\mathcal O_K$ 作为自由阿贝尔群的一组 $\mathbb Z$-基。

Example

$\{1,(1+\sqrt5)/2\}$ is an integral basis of $\mathbb Q(\sqrt5)$.

Usage and distinctions

$\{1,\sqrt5\}$ is a $\mathbb Q$-basis of that field but does not generate its full integer ring over $\mathbb Z$.

Recommended reading in this subject · Preparation & skip guidance

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Theorem 1.15 and text before Proposition 1.16 and Definition 1.17, printed pages 7–8 · Checked 2026-10-15

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§1.2.2，printed page 8 命题1.16前的 整基 及定义1.17 · Checked 2026-10-15

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