commutative ring

交换环

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

Translation evidence: Literature usage

Meaning in context

A unital ring whose multiplication satisfies ab=baab=ba for all elements.

乘法对任意两个元素都满足交换律的含幺环。

Example

Z[x]\mathbb Z[x] is commutative.

Usage and distinctions

The zero ring is allowed here, but excluded from fields and integral domains.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source基本概念 (sec:ring-basics), definition of 相反环, final clause R^op=R iff ab=ba naming 交换环 · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件基本概念 (sec:ring-basics), definition of 相反环, final clause R^op=R iff ab=ba naming 交换环 · Checked 2026-10-15
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