… not only give rise to adjoint functors for constructing recollements … modules, complete
cotorsion pairs make it possible to produce special preenvelopes once we know special precovers …

… preenvelope). We also study the exchange properties of … with ∈ C is a monic C-precover
of , then it is a monic C-cover of … As to the second claim, note that we have an adjoint …

… module has a special maximal CM precover. In this paper, we prove the existence of special
maximal CM preenvelopes … , which we claim is a left adjoint of the inclusion G : MCM → mod…

… This fact – discovered by Salce [34] – says that the mutually dual categorical notions of a
special precover and a special preenvelope are tied up by the homological tie of a cotorsion …

… -modules. Subsequently, in 1981 Enochs proved that any precovering class of modules closed
… L\) can be naturally extended to a pair of adjoint functors \(\Phi :\mathsf B\longrightarrow \…

… is devoted to preenvelopes and precovers of modules over a … of left A-modules and D be a
class of left B-modules, we prove … to see that p is a left adjoint of q and h is a right adjoint of q. …

… module categories. In particular we prove that every deconstructible class of modules is
precovering… M is necessarily an X-precover while the inflation M ↣ Y is a Y-preenvelope. We will …

… The rings whose simple right modules have a projective preenvelope are … homomorphism
φ: A → M is an ℳ-precover of M if A ∈ ℳ and the abelian … by the standard adjoint isomorphism. …

… A C-precover φ : C → M of M is said to be a C-cover if every … Dually we have the definitions
of a C-preenvelope and a C-… precovers and the cokernels of min-flat preenvelopes, we …

… ) in this category to be precovering, we need the class of flat discrete modules to be closed
… tensor product of modules) is precovering (see [2, Corollary 4.8]). Our type of precovers are …