… special precover sequences for all objects E ∈ E if and only if it admits special preenvelope
… in two exact categories connected by a pair of adjoint functors. It should be compared to …

… the stability of Gorenstein injective pre-envelopes and Gorenstein projective precovers
between the category of Amodules and the category of A#HL-modules. Moreover, we establish …

… a cotorsion preenvelope; a preenvelope is defined in a manner dual to that of a precover [37…
In other words, the functor F ↦→ F is the left adjoint of the inclusion functor from ((R-mod)op, …

… modules over Noetherian rings and contraadjusted modules over both Noetherian and
non-Noetherian rings, from our geometric standpoint. Flat cotorsion modules, … adjoint. Let D = lim …

… modules and sheaves are ubiquitous in algebraic geometry: if S is a finitely presented
commutative R-algebra which is flat as an R-module, then S is a very flat R-module… of a flat module …

… -modules) are equivalent under Foxby equivalence. For a commutative Noetherian ring R
and a semidualizing R-module C, it is shown that a finitely generated R-module … C-precover of …

… dimensions using adjoint precovers and adjoint preenvelopes of modules. … left 𝒞 -adjoint
resolutions of modules which are related to 𝒞 -adjoint preenvelopes and 𝒞 -adjoint precovers. …

… precover of M as a left A-module if and only if it is a special FP-projective precover of M as
a left A#σH-module … Then any left A-module has an FP-projective preenvelope if and only if …

… F-precover and F-cover are defined dually. Since in this paper we shall deal only with
preenvelopes … out to be very useful in the study of adjoints in the homotopy category of an abelian …

… F-precover and F-cover are defined dually. Since in this paper we shall deal only with
preenvelopes … out to be very useful in the study of adjoints in the homotopy category of an abelian …