---
tag: 4SPKGZBTTT
kind: concept
name: Algebraically closed group
aliases: [closed-group]
sources:
  - wikipedia: en:7156954@r1312536614
    locator: Algebraically closed group
    note: adopted
    mention: wikipedia://en/7156954
    sections: [Summary]
same_as:
  wikidata: Q4724025
  wikipedia: Algebraically closed group
inventory: [FHH5XKCN46]
---

## Summary

In group theory, a group $A$ is **algebraically closed** if any [[finite set|070R982G4B]] of equations and inequations that are applicable to $A$ have a solution in $A$ without needing a group extension. This notion will be made precise later in the article in § Formal definition.