Rational divisible hull ($G{\otimes }_{\mathbb{Z}}\mathbb{Q}$)

For a torsion-free abelian group $G$, its rational divisible hull is $G{\otimes }_{\mathbb{Z}}\mathbb{Q}$. It consists of fractions $g/n$, with $n>0$ and $g/n=h/m$ exactly when $mg=nh$. The natural map $G\to G\otimes \mathbb{Q}$ is injective. Every homomorphism from $G$ into a torsion-free divisible Abelian group extends uniquely through this hull.