  A ring $R$ is called left GF-closed, if the class of all Gorenstein flat left
$R$-modules is closed under extensions. The class of left GF-closed rings
includes strictly the one of right coherent rings and the one of rings of
finite weak dimension.
  In this paper, we investigate the Gorenstein flat dimension over left
GF-closed rings. Namely, we generalize the fact that the class of all
Gorenstein flat left modules is projectively resolving over right coherent
rings to left GF-closed rings. Also, we generalize the characterization of
Gorenstein flat left modules (then of Gorenstein flat dimension of left
modules) over right coherent rings to left GF-closed rings. Finally, using
direct products of rings, we show how to construct a left GF-closed ring that
is neither right coherent nor of finite weak dimension.
