… (2) Every finitely generated module has a pre-envelope with … A finitely generated module
M that satisfies these equivalent … , then N is still finitely generated and M is Gorenstein flat by …

… ) be a local ring and M a finitely generated R-module. So R (+… and Gorenstein rings,
homological dimension, multiplication … there is an R-module monomorphism j: M → A satisfying A …

… ring, then finitely generated max-projective right À-modules … R satisfies DCC on principal left
ideals;(3) Any left module M … (complete) if every right R-module has a (E-envelope and an g-…

… T-modules using duality pairs in A-Mod and B-Mod respectively. Then we characterize when
a left T-module is Gorenstein DT -projective, Gorenstein … Theorem 3.8 are satisfied. Thus the …

… , Gorenstein or regular. A sample result: Let (R, m) be a local Noetherian ring, M a finitely
generated R-module … As IR(k), the injective envelope of k, is a canonical R-module, it follows …

… finitely generated modules over non-commutative rings by Enochs and collaborators who
defined the central notion of Gorenstein projective module … examples of rings satisfying that the …

… to finitely generated modules over Gorenstein local rings. … , we will observe finitely generated
G-projective modules, and … right minimal if any endomorphism f :M → M satisfying ρ = ρf …

… of totally reflexive modules, which are also called modules of Gorenstein dimension zero or
finitely generated Gorenstein projective modules. There is … Each module X in X satisfies Exti …

… ∞ 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”, …