# Definition:Free Abelian Group

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## Definition

Let $G$ be an abelian group.

$G$ is a **free abelian group** if and only if the $\Z$-module associated with $G$ is a free $\Z$-module.

That is, $G$ is a **free abelian group** if and only if it has a basis over $\Z$.

## Sources

This needs considerable tedious hard slog to complete it.In particular: proper linkTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

- 2011: Michael Artin:
*Algebra*: Chapter 14: Linear Algebra in a Ring: 14.2. Free Modules