… rings, a module M having finite Gorenstein flat dimension is equivalent to M having finite
Gorenstein projective … the Gorenstein projective modules (whether finitely generated or not) and …

… all left modules over a right n-coherent ring have Gorenstein n-… > 0 or n = ∞) if every finitely
generated submodule of a free right (… Dually, we have the definition of a C-(pre) envelope. C-…

… certain rings all finitely generated modules have Gorenstein … by finitely generated Gorenstein
projective modules (left and … then 0 : AT- »G is called a Gorenstein injective envelope of N. …

… First of all, we will study the general theory of envelopes and … Cohen-Macaulay rings and
Gorenstein rings by the dual Bass … every finitely generated right R-module is finitely presented. …

… if each module M over a ring A has a Gorenstein projective … quotient K(ProA)/E(A) to satisfy
that each Hom set is in fact a set (… (i) The cohomology of D is bounded and finitely generated …

… rings (rings of finite global dimension), but to make the analogy complete a fourth condition,
dealing with non-finitely generated modules, is … it is also called the injective envelope of M. …

… n-tilting modules, n-cotilting modules, Gorenstein projective, … coherent ring [9] if every finitely
generated right ideal is finitely … the D-preenvelope φ is called a D-envelope of N. Dually we …

… 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 and all modules are unital. The notion of a “semidualizing … A finitely generated R-module
C is called semidualizing if the natural … is a complex Y of R-modules satisfying the following: …

… Throughout this paper, all rings are nonzero Gorenstein rings, ie, … have the definitions of a
C -preenvelope and a C -envelope. … sum of finitely generated Gorenstein projective modules. …