commutative local ring

交换局部环

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

Translation evidence: Literature usage

Meaning in context

A nonzero commutative ring with a unique maximal ideal.

具有唯一极大理想的非零交换环。

Example

Z(p)\mathbb Z_{(p)} has maximal ideal pZ(p)p\mathbb Z_{(p)}.

Usage and distinctions

Local does not mean finite or a ring of analytic functions; fields are local rings.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author sourcedefinition def:noncommutative-local-ring and immediately following paragraph, commutative specialization with a unique maximal ideal · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件一般扩域的赋值, paragraph after def:valuation-ring naming 局部环 · Checked 2026-10-14
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