… the class of Gorenstein flat modules over a right coherent rings, … The dual notion is that of
(pre-)envelopes: if E is a class, the … we assumed S was finitely generated and projective over R, …

… ring with a dualizing module, at least for finitely generated … a duality and that finitely generated
modules in the Auslander class … Preenvelopes, special preenvelopes and envelopes are …

… R is a local commutative Gorenstein ring, any finitely generated module M has a
complete … , Rings satisfying every finitely generated module has a Gorenstein projective (pre)envelope, …

… left Gorenstein rings, which are defined as rings satisfying that … Dually, we have the definitions
of X-(pre)envelope, special X-… in which each RPi is finitely generated free. We denote by …

… Throughout this paper, all rings are nonzero Gorenstein rings, ie, … with finite self-injective
dimensions from both sides, and all … sum of finitely generated Gorenstein projective modules. …

… , if every object has an X-(pre)envelope, we say that X is (pre)… by a strongly Gorenstein flat
module, a module M such that … subprojectivity domains of finitely generated modules coincide. …

… an X-cover if every R-morphism ψ : X → X satisfying ϕ = ϕψ is … we have the definitions of an
X-(pre)envelope and an X-(pre)… coherent ring with NB and MA finitely generated projective. (1…

… ∞ fin (of finitely generated modules of finite Gorenstein projective … ring R and Λ is finitely
generated as a module over R. … of modules, also known as the “theory of covers and envelopes”, …

… between the (pre)covers (respectively, (pre)envelopes) in C … We prove that a finitely generated
left R-module M is τ-rigid (… if all its finitely generated Gorenstein projective modules are …

… satisfies (DARC), then it also satisfies (ARC). We prefer to … , CM( ) contains finitely generated
Gorenstein projective modules as a … Gorenstein ring, the Gorenstein injective envelope of an …