… is introduced, and the relationships of this kind of modules with the FP n -flat preenvelope
of the right R-modules and the FP n -flat adjoint preenvelope of the left R-modules are given. …

… under isomorphisms, an F-precover of an object X of C is a … Let us illustrate with injective
preenvelopes Lα → Eα where … H is a left adjoint to the forgetful functor (−)H [14, Proposition …

… projective precover. … preenvelopes, one may think of using the well-known results of Neeman
asserting the existence of left adjoints under some assumptions and then use this adjoint to …

… It has become clear that adjoint functors between homotopy … to taking precovers or
preenvelopes using completeness of … X of R-modules has a Gorenstein injective preenvelope and …

… 4, using (n, d)-flat preenvelopes and (n, d)-injective precover, … by the existences of these
preenvelopes and precovers. In Sec. 5, … Then every left R-module has an (n, d)-flat preenvelope …

… modules over a ring R are strongly linked to approximation theory (preenvelopes and
precovers… and S is isomorphic to the endomorphism ring of the left adjoint L(B). Moreover, S is the …

… locally finitely generated R-modules. Indeed, we prove that in this context, every module X
in Mod R … has a left adjoint Fλ : MOD A → MOD B which restricts to finitely generated (= finite …

… On one side, we shall show that Freyd's adjoint functor … The dual concepts are p-precover
(or right p-approximation), … We prove that every object A of e has a Copres (M)-preenvelope, …

… object of A has a special C-preenvelope and a special F-precover (resp., a C-envelope and
… unitary R-modules. The term R-module will be used to indicate a left R-module. RM denotes …

… module with some extra conditions is precisely a module RC such that the Bass class BC (R)
coincides with the class of modules of … the existence of precovers and preenvelopes of the …