---
tag: 0WJX8MGG37
kind: concept
name: Free abelian group
msc: [20K15, 20K20]
sources:
  - url: https://en.wikipedia.org/wiki/Free_abelian_group
    locator: lead section
same_as:
  wikidata: Q1454111
  wikipedia: Free abelian group
---

## Summary

A free abelian group is an abelian group with a basis. Each element is an integer combination of finitely many basis elements in exactly one way.
The free abelian group of finite rank $n$ is isomorphic to $\mathbb{Z}^n$.