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