---
tag: 01VH21EV6F
kind: concept
name: Prime element
msc: [13A05]
sources:
  - url: https://en.wikipedia.org/wiki/Prime_element
    locator: lead section
same_as:
  wikidata: Q240651
  wikipedia: Prime element
---

## Summary

A prime element of a commutative ring is a nonzero nonunit $p$ with the following property. If $p$ divides a product, then $p$ divides one of the factors.
The [[definition of a prime element|0MNHXBSX3M]] gives the conditions.