irreducible element

不可约元

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

Translation evidence: Literature usage

Meaning in context

A nonzero nonunit $r$ in a domain such that $r=ab$ forces $a$ or $b$ to be a unit.

整环中不能分解为两个非单位乘积的非零非单位元素。

Example

$2$ is irreducible in $\mathbb Z[\sqrt{-5}]$.

Usage and distinctions

Irreducible need not mean prime in an arbitrary domain.

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, opening clause defining nonzero nonunit 不可约 elements · 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, opening clause defining nonzero nonunit 不可约 elements · Checked 2026-10-15

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.