Generating a power basis over a Dedekind ring

Let R be a Dedekind ring, K its quotient field, L a separable finite extension over K, and OL the integral closure of R in L. In this paper we provide a “practical” criterion that tests when a given α∈OL generates a power basis for OL over R (i.e. when OL=R[α]), improving significantly a result in this direction by M. Charkani and O. Lahlou. Applications in the context of cyclotomic, quadratic, biquadratic number fields, and some Dedekind rings are provided.