Another Gorenstein analogue of flat modules.

A rightR-moduleMis called glat if any homomorphism from any finitely presented rightR-module toMfactors through a finitely presented Gorenstein projective rightR-module. The concept of glat modules may be viewed as another Gorenstein analogue of flat modules. We first prove that the class of glat rightR-modules is closed under direct sums, direct limits, pure quotients and pure submodules for arbitrary ringR. Then we obtain that a rightR-moduleMis glat if and only ifMis a direct limit of finitely presented Gorenstein projective rightR-modules. In addition, we explore the relationships between glat modules and Gorenstein flat (Gorenstein projective) modules. Finally we investigate the existence of preenvelopes and precovers by glat and finitely presented Gorenstein projective modules. [ABSTRACT FROM AUTHOR]