Let $f: R \to S$ be a ring homomorphism. When is the induced map $f^{*}: \operatorname{Spec}(S) \to \operatorname{Spec}(R)$ on topological spaces a covering map?
More precisely, are there any interesting necessary or sufficient (algebraic) conditions on $f$ for $f^*$ to be a covering map? Note that obviously a covering map is surjective, so every prime ideal of $R$ must be a contracted ideal.
I would also appreciate it if someone could only explain example of covering spaces in this setting. On this wikipedia page one can find the assertion
The map of affine schemes ${\text{Spec}}(\mathbb {C}[x,t,t^{-1}]/(x^{n}-t))\to {\text{Spec}}(\mathbb {C} [t,t^{-1}])$ forms a covering space with $\mathbb {Z} /n$ as its group of deck transformations.
But I cannot see why this true. Perhaps someone could start by examining this example.