… a C-precover, then the class C is called precovering. The dual notions are preenvelope and
preenveloping … Let us note that the adjoint pairs of functors on sheaves (j∗, j∗), (h∗,h∗) yield …

… adjoint ω-coreflexive) if µN is a monomorphism (resp. an isomorphism) ([TH3]). … ) Any
module in Mod R has a special U-precover. (2) Any module in Mod R has a special V-preenvelope. …

… propriétés équivalentes de ces modules sur des anneaux nX-… les modules nX-injectives de
Gorenstein et les modules nX-… flat R-modules, we speak simply of the flat preenvelope of M. …

… of modules, the significance of Gorenstein projective modules … An X -precover φ is said to
be special if it is an epimorphism … Pre-envelopes, special pre-envelopes, and envelopes are …

… FP-injective modules, so we recall first that a module A is … It is known that a precovering class
that is also closed under … Thus \(X \rightarrow I\) is a special Ding injective preenvelope of X. …

… three functors which form two adjoint pairs between F and G ; … ϕ → w in F with w ∈ W is
called: • A W -preenvelope of f if it … module and viewing it as a Φ-module through θ. There is a left …

… 妻0 : D −→ D妻0 and τ>0 : D −→ D>0 , which are right and left adjoint to the inclusion … Such
an algebra will be called a finite length algebra when it has finite length as a K-module (note …

… an X -precover, then X is called a precovering class of A . An X -… X -preenvelopes,
preenveloping and enveloping classes are … Let prj-Λ denotes the class of projective Λ-modules. It …

… preenvelopes. By constructing duality pairs with respect to Gorenstein (L, A)-injective
modules and Gorenstein (L, A)-flat modules … X is precovering if every object of A has an X-precover. …

… pre-covers and left approximations for pre-envelopes, are constructions developed as early
as 1953 by Eckman and Schopf in [22]. They show that each module … pair of adjoint functors …