integral domain

整环

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

Translation evidence: Literature usage

Meaning in context

A commutative unital ring with $1\ne0$ in which $ab=0$ implies $a=0$ or $b=0$.

满足 $1\ne0$ 且无非零零因子的交换含幺环。

Example

$\mathbb Z[\sqrt{-5}]$ is a domain.

Usage and distinctions

A domain need not be a field or have unique factorization.

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Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source几类特殊的环, definition of 整环 (no nonzero zero divisors), under the section's explicit nonzero-ring convention · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件几类特殊的环, definition of 整环 (no nonzero zero divisors), under the section's explicit nonzero-ring convention · Checked 2026-10-15

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