Generating a power basis over a Dedekind ring

Abstract

Let R be a Dedekind ring, K its quotient field, L a separable finite extension over K , and O L the integral closure of R in L . In this paper we provide a “practical” criterion that tests when a given α ∈ O L generates a power basis for O L over R (i.e. when O L = 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.