Corrigendum to “The twisted group ring isomorphism problem over fields”

We rectify Theorem 3.4 of [1] which gives a relation between the isomorphism types of a group algebra FG of a finite abelian group G over a field F of characteristic 0, the second cohomology group H2(G, F*) and the isomorphism type of G. We show how this relation depends on the behavior of F under extensions by roots of unity.