class number of a number field

数域的类数

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

Translation evidence: Literature usage

Meaning in context

The finite cardinality $h_K=|\operatorname{Cl}(K)|$ of the ideal class group of a number field $K$.

数域 $K$ 的理想类群的有限阶数 $h_K=|\operatorname{Cl}(K)|$。

Example

$h_{\mathbb Q(i)}=1$.

Usage and distinctions

Class number one means every ideal is principal; it does not mean the field has degree one over Q.

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 1.3.2, Theorem 1.38 and following paragraph, printed page 15 · 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定理1.38后，printed page 15 类数 · Checked 2026-10-14

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