  We give necessary and sufficient conditions in order for the class of
projectively coresolved Gorenstein flat modules, $\mathcal{PGF}$, (respectively
that of projectively coresolved Gorenstein $\mathcal{B}$ flat modules,
$\mathcal{PGF}_{\mathcal{B}}$) to coincide with the class of Ding projective
modules ($\mathcal{DP})$. We show that $\mathcal{PGF} = \mathcal{DP}$ if and
only if every Ding projective module is Gorenstein flat. This is the case if
the ring $R$ is coherent for example. We include an example to show that the
coherence is a sufficient, but not a necessary condition in order to have
$\mathcal{PGF} = \mathcal{DP}$. We also show that $\mathcal{PGF} =
\mathcal{DP}$ over any ring $R$ of finite weak Gorenstein global dimension
(this condition is also sufficient, but not necessary). We prove that if the
class of Ding projective modules, $\mathcal{DP}$, is covering then the ring $R$
is perfect. And we show that, over a coherent ring $R$, the converse also
holds. We also give necessary and sufficient conditions in order to have
$\mathcal{PGF} = \mathcal{GP}$, where $\mathcal{GP}$ is the class of Gorenstein
projective modules.

Rings and Algebras