ABSTRACT
The only type of Gorenstein resolutions that are known to exist over arbitrary ringa (associative with identity) are the Gorenstein flat left resolutions. Unlike the case of Gorenstein flat precovers, the existence of the Gorenstein flat preenveopes is still an open problem. There is a result due to Enochs and López-Ramos showing that if the class of Gorenstein flat modules is closed under direct products then it is preenveloping. Since the class of Gorenstein flat modules is a Kaplansky class (over any ring R), a sufficient condition for the existence of Gorenstein flat preenvelopes is that the class of Gorenstein flat modules also be closed under direct products.
