  In this work, we study those differential graded algebras (DGAs) that arise
from ring spectra through the extension of scalars functor. Namely, we study
DGAs whose corresponding Eilenberg-Mac Lane ring spectrum is equivalent to
$H\mathbb{Z} \wedge E$ for some ring spectrum $E$. We call these DGAs extension
DGAs. We also define and study this notion for $E_\infty$ DGAs.
  The topological Hochschild homology (THH) spectrum of an extension DGA splits
in a convenient way. We show that formal DGAs with nice homology rings are
extension and therefore their THH groups can be obtained from their Hochschild
homology groups in many cases of interest. We also provide interesting examples
of DGAs that are not extension.
  In the second part, we study properties of extension DGAs. We show that in
various cases, topological equivalences and quasi-isomorphisms agree for
extension DGAs. From this, we obtain that dg Morita equivalences and Morita
equivalences also agree in these cases.
