Let F be an algebraic function field with a finite field of constants and fix a place  of F. Define A to be the ring of elements in F that are regular at every place except possibly . In particular, A is a Dedekind domain and it is discrete in F (with the topology induced by ).
Consider an algebraic function field F with a finite constant field and a fixed point  in F. Define A as the subring of F consisting of elements that remain integral everywhere except potentially at .