unique factorization domain

唯一分解环

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

Other names / variants: UFD

Translation evidence: Literature usage

Meaning in context

A domain in which each nonzero nonunit factors into irreducibles uniquely up to factor order and multiplication by units.

每个非零非单位都能不可约分解，且除因子次序和单位因子外分解唯一的整环。

Example

Z[x]\mathbb Z[x] is a UFD.

Usage and distinctions

Existence of factorizations alone does not imply their uniqueness.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source唯一分解性 (sec:UFD), definition def:UFD, 唯一分解环 clause and uniqueness modulo units and factor order · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件唯一分解性 (sec:UFD), definition def:UFD, 唯一分解环 clause and uniqueness modulo units and factor order · Checked 2026-10-15
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