… and obtain some closure properties of Gorenstein f-projective R-modules. As a … when every
finitely generated R-module has a finitely generated Gorenstein projective (pre)envelope. For …

… If M is a finitely generated module over a local ring S, and S b … E is the injective envelope of
the R-module k; furthermore, in … All of the hypotheses of Theorem 1.2 are satisfied by the ring …

… 93 be a covariantly finite subcategory of 9?, satisfying the following: … , then the injective
envelope of A is finitely generated. This … envelopes of the isoclasses of simple modules is a finitely …

… C-envelopes and 'C-covers of finitely generated modules exist … Since injective modules form
a subclass of C', we can form … is a local ring aud tLat all modules are finitely generated. The …

… Just as a ring is called Gorenstein when it is n-Gorenstein for … results concerning existence
of covers and envelopes. … G is finite, U preserves finitely generated modules. Since U is …

… 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 …

… ring R various classes of relative Gorenstein projective R-… f in (finitely generated modules of
finite Gorenstein projective dimension… Dually, one has the notions of (pre)envelopes and (pre)…

… 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)…

… Gorenstein ring every finitely generated module M has a complete … each morphism ϕ: F →
F satisfying f ○ ϕ =f is an automorphism. If … Suppose that M has a projective envelope. Then a …

… of special Gorenstein projective precovers over such a ring and we … of Gorenstein projective
covers for any finitely generated … a limit ordinal, we have (j>a-\,a-2 • X —• X satisfying the …