---
tag: 0PF6TM8TWT
kind: concept
name: Algebraically closed field
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Algebraically_closed_field
    locator: lead section
same_as:
  wikidata: Q1047547
  wikipedia: Algebraically closed field
---

## Summary

An algebraically closed field is a field in which every nonconstant polynomial has a root.
The complex numbers are the main example.
The [[definition of an algebraically closed field|02SJG1HC32]] gives equivalent conditions.