… We say that an Ä-module M is r-injective if ExtlR(T r-torsion ^-module T. We will denote by …
We take a ./^-precover of Af which kernel is »/«^-reduced, e: JEo - ► Af. Then 0 E0 - ¡ ► Af is a …

… module M admits a right X-approximation, then X is called a contravariantly finite subcategory,
or X is a precovering … By the adjoint pair one can see that R+ is an injective left R-modules. …

… modules that arise in this way. Namely, a tilting module T is equivalent to a tilting module S
… (2) ⇒ (1) : By the definition of a preenvelope, we have that SR belongs to U⊥. Since U⊥ is …

… 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. …

… modules over a concealed canonical algebra of domestic or tubular type. In the domestic
case, such tilting modules are … modules and a description of the indecomposable pure-injective …

… On one side, we shall show that F'reyd's adjoint functor … The dual concepts are 3-precover
(or right 3-approximation), … Then it is clear that p is an 3-preenvelope of A, and we shall …

… Enochs proved that a precovering class of modules closed under direct limits is … adjoint
functors to the identity inclusions of these full subcategories into the category of left R-modules. In …

… Accordingly, the left and right adjoint functors to the forgetful functor Z0(B–Mod) −→ B∗–…
called a special precover sequence. A short exact sequence (4) is called a special preenvelope …

… This connection to adjoint functors is our motivation to studying complete cotorsion pairs in
… of flat OX-modules admits a flat precover and a dg-cotorsion flat preenvelope; see Theorem …

… modules over commutative hereditary Noetherian rings is given. Rings all (cyclic) modules …
Over a right Noetherian ring every left module is rugged or flat if and only if every right module …