It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …

Mod ª Ex C, Ab, M¬ Hom y, M my Ž. Ž. Ž. is an equivalence. Thus we can replace a-module
by an exact functor Ž. op C ª Ab. Of course, since the work of Auslander, it has been common …

Several authors have studied the filtered colimit closure \varinjlimB of a class B of finitely
presented modules. Lenzing called \varinjlimB the category of modules with support in B …

Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …

In an arbitrary Grothendieck category, we find necessary and sufficient conditions for the
class of FP n-injective objects to be a torsion class. By doing so, we propose a notion of n …

We prove the following results for the subcategories of an abelian category: 1) The full
subcategory whose objects are kernels of the maps between two covariantly finite …

Let R be a commutative Noetherian ring and let G be the category of modules of G-
dimension zero over R. We denote the associated stable category by G. We show that the …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …