zero divisor

零因子

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

Translation evidence: Literature usage

Meaning in context

A nonzero element of a commutative ring whose product with some nonzero element is zero.

交换环中能与某个非零元素相乘得到零的非零元素。

Example

2ˉ\bar2 is a zero divisor in Z/6Z\mathbb Z/6\mathbb Z.

Usage and distinctions

Some authors include zero itself; this record excludes it explicitly.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source几类特殊的环, same paragraph's left/right 零因子 definition requiring nonzero r and a; commutative specialization · 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, same paragraph's left/right 零因子 definition requiring nonzero r and a; commutative specialization · Checked 2026-10-15
Edit source / propose a PRReport a correction

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