prime element

素元

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

Translation evidence: Literature usage

Meaning in context

A nonzero nonunit $p$ in a domain such that $p\mid ab$ implies $p\mid a$ or $p\mid b$.

整环中整除乘积就必整除某一因子的非零非单位元素。

Example

$x$ is prime in $F[x]$.

Usage and distinctions

Prime implies irreducible; the reverse requires extra factorization hypotheses.

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), paragraph beginning 如果整环 R 中的非零元 p, after def:UFD, defining 素元 by the product-divisibility condition · 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), paragraph beginning 如果整环 R 中的非零元 p, after def:UFD, defining 素元 by the product-divisibility condition · Checked 2026-10-15

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