Addendum to: Reductions of algebraic integers [J. Number Theory 167 (2016) 259–283]

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K × . We consider Kummer extensions of G of the form K ( ζ 2 m , G 2 n ) / K ( ζ 2 m ) , where n ⩽ m . In the paper by Debry and Perucca (2016) [1] , the degrees of those extensions have been evaluated in terms of divisibility parameters over K ( ζ 4 ) . We prove how properties of G over K explicitly determine the divisibility parameters over K ( ζ 4 ) . This result yields a clear computational advantage, since no field extension is required.