… Moreover, for any finitely generated -module M, we denote by … = 0, we have M ⊆ Mσ ⊆ E(M)
for an injective envelope E(M) … pair (mod- ,e) in turn satisfies the hypotheses 4.1: Indeed, the …

… −1 (X) =: Cokerf if f is right minimal, ie if f is an injective envelope of X. … to denote the category
of finitely generated right modules, … Gorenstein projective modules in mod . Set G := ⊕n …

… Note that F-envelopes and F-covers may not exist in … rings. One of the main reasons is that
it always provides a resolution of a finitely generated module by finitely generated projective …

… module has a FI-flat cover and FI-cotorsion envelope and we prove that the FI-flat envelope
of a module … that, the FIcotorsion of a ring R is ≤ 1 if and only if every FI-flat R-module has a …

… ring with identity and R-Mod is the category of left R-modules. … - Mod such that each P i is
finitely generated and projective. … the existence of (pre)covers and (pre)envelopes relative to a …

… the impetus for all of this. We recall that, for modules over a ring R, a cotorsion module C is
… Let B ֒→ RB be a Gorenstein injective approximation (special pre-envelope) of the sheaf B. …

… a ring Λ over which every finitely generated module has an … Since MCM R # -modules
satisfy the Krull–Remak–Schmidt … Iwanaga–Gorenstein, and we identify the relative Gorenstein-…

… of self extensions of finitely generated modules over commutative Noetherian rings. The aim
of … [5] proved that M is Gorenstein projective if and only if the G-dimension of M is zero (see …

… Then projective covers and injective envelopes in \(\mathscr {… of Gorenstein projectives over
an Iwanaga–Gorenstein ring [… the category of finitely generated Gorenstein projectives over …

… ) C is Gorenstein injective if and only if \(C_n\) is a Gorenstein … ring with identity and all
modules are unitary left R-modules. We … of finitely generated and finitely presented N-complexes. …