… the concepts of adjoint preenvelopes and adjoint precovers of modules and some … relationships
between adjoint preenvelopes, adjoint precovers and preenvelopes and precovers were …

… Moreover, if the only such g are automorphisms of F when F = F and f = φ, then the D-preenvelope
φ is called a D-envelope of M. Dually we have the notions of a D-precover and a D-…

… Also we define a new tensor product in the category of complexes which is left adjoint of
the … £precover. In a similar manner, we see that every object N of A has a special Çpreenvelope. …

… functor), and we let St : A/T → A be the fully faithful right adjoint of Qt. If A = Mod-R is the
category of right R-modules over a ring R, then we can consider the ring of quotients ψ : R → Rt …

… by a set of modules G, then F is precovering and C is preenveloping. More precisely, [GT06,
Theorem 3.2.1] asserts that each module has a C-preenvelope with cokernel in Filt −G. …

… precovers and Gorenstein injective preenvelopes is an active subject of study nowadays, not
only in the category of modules … of modules, those of representations of quivers by modules, …

… Dually are defined X-preenvelopes and X-… of modules G such that C= G⊥). This is due to
the fact that a cotorsion pair generated by a set always provide for precovers and preenvelopes…

… Using the above adjoint associativity again we conclude that … Suppose every module M has
a special GIB-preenvelope. … to show every module M has a special PGFB-precover. But by …

… preenvelopes and precovers in the category \(_{R}{\mathcal {E}}\) of short exact sequences
of left R-modules. Let \… F is the left adjoint of the functor G. Then Theorem 2.1(1) is clear by the …

… called precovering if every M ∈ G has an Aprecover. Dualizing the definition, we obtain the
notion of an A-preenvelope: … However, this functor, being right adjoint to an exact functor (the …