  We characterize finite Galois extensions $K$ of the field of rational numbers
in terms of the rings ${\rm Int}_{\mathbb{Q}}(\mathcal O_K)$, recently
introduced by Loper and Werner, consisting of those polynomials which have
coefficients in $\mathbb{Q}$ and such that $f(\mathcal O_K)$ is contained in
$\mathcal O_K$. We also address the problem of constructing a basis for ${\rm
Int}_{\mathbb{Q}}(\mathcal O_K)$ as a $\mathbb{Z}$-module.
