---
tag: 0X6AB5P3G1
kind: concept
name: Algebraic closure
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Algebraic_closure
    locator: lead section
same_as:
  wikidata: Q428290
  wikipedia: Algebraic closure
---

## Summary

An algebraic closure of a field $K$ is an algebraic extension of $K$ that is algebraically closed.
It exists and is unique up to an isomorphism that fixes $K$.
The [[definition of an algebraic closure|0MCXX29HWY]] states it.