… We show (Theorem 4.2) that a ring R is left n-perfect if and only if every Gorenstein flat left
R-… Perfect if every module has an X-cover and a Y-envelope. • Cogenerated by a set if there is …

… semidualizing module over a commutative Noetherian ring R. … Covers and Envelopes Let X
be a class of R-modules and M … of finitely generated Gorenstein projective R-modules for any …

… 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 …

… The theory of finitely generated relative (co)tilting modules has … over virtually Gorenstein
CM-finite rings. The main result of … ) is satisfied over CM-finite virtually Gorenstein artin algebras. …

… R and S, are given by a bimodule RPS, such that RP is a finitely generated projective generator
… , D-Gorenstein, static, and A,(k)-modules, as well as covers and envelopes of modules... …

… If the equivalent conditions in Proposition 2 are satisfied, then we say that the module M
has … In this section, we characterize those rings over which all modules have finite PGF-…

… that a module M over a commutative ring R is weak Gorenstein … resolution by finitely generated
projectives. Note that if R is … a weak Gorenstein cotorsion envelope of a right R-module M, …

… -free finitely generated Gorenstein-projective module, then … finitely generated modules without
extensions with the ring … envelope of R/rad(R). The Jacobson radical of Λ is denoted by r. …

… G–dimension satisfies an analogue of the Auslander–… Only when a module has bistructure,
do we include the rings in … complex of finitely generated Gorenstein projective R–modules, …

… in the specific setting of a Gorenstein ring. Applying similar … -envelopes). Instead, our
approach relies on a combination of … direct limit of finitely generated projective modules. One can …