… Gorenstein projective modules (whether finitely generated or not) and Gorenstein injective
modules over arbitrary rings 5… of (pre)envelopes and (pre)covers with respect to the classes of …

… Gorenstein projective preenvelopes. We show, among other things, that the finitely generated
Gorenstein projective modules … Existence of G-envelopes now follows from Theorem 1.6(iii)…

… Moreover we assume all modules are finitely generated. In … of minimal projective resolutions,
or "projective envelopes." … In summary: A local ring satisfying (a) which is not Gorenstein …

… of Gorenstein projective and injective modules that we derive … but all the syzygies of a
finite module to be finitely generated. … We say it has enough injectives if it satisfies the dual …

… finitely generated and finitely presented modules (over a ring R… A ring R satisfying the
equivalent conditions above is said to … if every left R-module has an epimorphic FPn-Flatenvelope. …

… For any finitely generated R-module M, we have the natural … If in the definition, (1) is satisfied,
then we call qþ a flat precover. … rings for which every flat module has an injective envelope …

… D over a commutative ring R, we investigate the relationship … C such that each Pi is finitely
generated projective; (2) The natural … White, Gorenstein projective dimension with respect to a …

… Noetherian rings, the investigation of covers and envelopes will … X is called an X-envelope
of M if the following are satisfied: … Over such a ring, a finitely generated module P is called zero …

… ring R and briefly recapitulate some definitions. The finitely generated Gorenstein projective
modules … Then each finitely generated R-module has an ¿-envelope by [16, Prop. 2.3(3)], …

… In this process, finitely generated modules should in general be replaced by finitely presented
mod… Note that F-envelopes and F-covers may not exist in general, but if they exist, they are …