Let $D$ be an abelian group, regarded as a $\mathbb{Z}$-module under its usual scalar multiplication. Then $D$ is an injective $\mathbb{Z}$-module if and only if $D$ is divisible; that is, if and only if for every $d \in D$ and every integer $n \geq 1$, there exists $x \in D$ such that $n x = d$.