We prove that Vopěnka's Principle implies that for every class X of modules over any ring,
the class of X-Gorenstein Projective modules (X-GP) is a precovering class. In particular, it is …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

\emph {Approximation Theory} uses nicely-behaved subcategories to understand entire
categories, just as projective modules are used to approximate arbitrary modules in classical …

It is a well-known result of Auslander and Reiten that contravariant finiteness of the class P∞
fin (of finitely generated modules of finite projective dimension) over an Artin algebra is a …

Given a two-sided noetherian ring $ A $ with a dualizing complex, we show that the big
finitistic dimension of $ A $ is finite if and only if every bounded below Gorenstein-projective …

We use the framework of Tensor-Hom-Cotensor situations to present a generalization to
abelian categories of the flat cotorsion theory for modules over a ring. Using the generalized …