cyclotomic number field

分圆域

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

Translation evidence: Literature usage

Meaning in context

A field $\mathbb Q(\zeta_n)$ generated by a complex root of unity $\zeta_n$ of exact order $n$.

由一个阶恰为 $n$ 的复单位根 $\zeta_n$ 生成的数域 $\mathbb Q(\zeta_n)$。

Example

$\mathbb Q(\zeta_4)=\mathbb Q(i)$.

Usage and distinctions

Different orders can define the same field: $\mathbb Q(\zeta_3)=\mathbb Q(\zeta_6)$.

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Section 1.2.3, Exercise 1.2.8(2) and Section 1.2.4, Proposition 1.22 · 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§1.2.3 习题1.2.8(2) 分圆域；§1.2.4，printed pages 10–11 · Checked 2026-10-14

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