---
tag: 0CMD0BCH8T
kind: concept
name: Principal ideal domain
aliases: [pid]
msc: [13F10]
sources:
  - url: https://en.wikipedia.org/wiki/Principal_ideal_domain
    locator: lead section
same_as:
  wikidata: Q1143969
  wikipedia: Principal ideal domain
---

## Summary

A principal ideal domain is an integral domain in which every ideal is generated by one element.
The integers and the polynomials over a field are examples.
The [[definition of a principal ideal domain|0RZYDVZ475]] gives the conditions.