Rational divisible hull
= Rational divisible hull
{title2=$G\otimes_{\mathbb Z}\mathbb Q$}
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.