Let $R$ be an integral domain, and $K := \text{Frac}(R)$ is the field of fractions of $R$ . Then $K$ is a torsion-free $R$ -module (see The Stacks project tag/0549).

Proof. [local-0]

We want to show that the only torsion element of $K$ is $0$ . Every element of $K$ has the form $\frac{a}{s}$ where $s \ne 0$ , now suppose $\frac{a}{s}$ is a torsion. Then there exists a $r \ne 0 \in R$ such that

r \frac{a}{s} = \frac{ra}{s} = 0 \in K

which leads

ra = 0 \in R

in an integral domain, this leads $r = 0$ or $a = 0$ , but $r \ne 0$ by definition, hence $a = 0$ . Which means $\frac{a}{s}$ is $0 \in K$ , be torsion is be zero in $K$ , $K$ is a torsion-free $R$ -module.