---
tag: 0CHS7RBD39
kind: concept
name: Euclidean domain
msc: [13F07]
sources:
  - url: https://en.wikipedia.org/wiki/Euclidean_domain
    locator: lead section
same_as:
  wikidata: Q867345
  wikipedia: Euclidean domain
---

## Summary

A Euclidean domain is an integral domain with a division with remainder, in which the remainder is smaller than the divisor for some size function.
The integers and the polynomials over a field are the main examples.
The [[definition of a Euclidean domain|0GJ2HRG95T]] gives the conditions.