… existence of special Gorenstein projective precovers over such a ring and we generalize
Auslander's last theorem about the existence of Gorenstein projective covers … Çpreenvelope. O …

… R-modules are special precovering, among them including the Gorenstein … Gorenstein
flat PGF(R) fulfils the same feature. We also introduce a new class of Gorenstein projective R-…

… , Gorenstein injective preenvelopes always exist. If, in addition, we want to get special Gorenstein
injective preenvelopes… condition holds then direct products of Gorenstein injectives are …

… global Gorenstein dimension. We also show the existence of X -Gorenstein projective … An
F -preenvelope of M can be defined dually. The first main result of Section 2 (see Theorem 2.8) …

… of Gorenstein projective dimension of complexes. Motivated by this concept we introduce
the definitions of complete Gorenstein projective resolutions and complete preenvelope-…

… Gorenstein-flat precover, and in [16], Šaroch and Stovicek proved … existence of
Gorenstein-injective preenvelopes. However, it is not known if every module has a …

… special preenvelopes once we know special precovers exist … special precovering or covering
under suitable conditions. The … which are flat, Gorenstein projective and Gorenstein flat. A …

… On the other hand, the existence of Gorenstein projective precovers and Gorenstein injective
preenvelopes is an active subject of study nowadays, not only in the category of modules …

… Gorenstein subcategory G(C ) of A , which is a common generalization of the notions of
modules of Gorenstein dimension zero (see [3]), Gorenstein projective … G(C )-preenvelopes. We …

… modules by Lemma 3.2, we can apply Lemma 3.1 with B = H⊥ to get a special H⊥preenvelope
M → X0 with X0 free of rank κ, for κ the number of generators of M. We can repeat this …