localization of a commutative ring

交换环的局部化

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

Translation evidence: Literature usage

Meaning in context

For a multiplicative set $S$, the universal ring $S^{-1}R$ receiving a map from $R$ that makes every member of $S$ invertible.

使指定乘性集的元素全变为可逆元并满足相应泛性质的环构造。

Example

$\mathbb Z[1/2]$ contains $3/8$ but not $1/3$.

Usage and distinctions

Zero divisors require $a/s=b/t$ to mean $u(ta-sb)=0$ for some $u\in S$.

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Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source交换环初探 (sec:comm-ring-intro), construction beginning 构作对乘性子集 S 的局部化 and proposition immediately after eqn:localization-zero giving its universal property · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件交换环初探 (sec:comm-ring-intro), construction beginning 构作对乘性子集 S 的局部化 and proposition immediately after eqn:localization-zero giving its universal property · Checked 2026-10-15

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