Valuations and Dedekind's Prague theorem (Q1840477)

The paper contains an effective proof of the following theorem of Dedekind: If \(f\) and \(g\) are polynomials in one indeterminate whose cofficients are algebraic numbers, and if all the coefficients of \(fg\) are algebraic integers, then the product of any coefficient of \(f\) with any coefficient of \(g\) is an algebraic integer. The proof is based on properties of the entailment relation of \textit{D. Scott} [Proc. Symp. Pure Math. 25, 411-435 (1974; Zbl 0318.02021)]. The authors also recover a result from Hilbert's Zahlbericht and present other applications of entailment relations.