Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

Given a finite dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ= A⊗ kk
Q/I, where kQ is the path algebra of Q over k and I is a monomial ideal. This paper is devoted …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

In this paper, we study completeness of cotorsion pairs in the category of complexes of R-
modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair …

Let (𝒳, 𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜.
We introduce a Gorenstein category 𝒢 (𝒳) and 𝒢 (𝒳)-resolution dimension of complexes …

The theory of finitely generated relative (co) tilting modules has been established in the
1980s by Auslander and Solberg, and infinitely generated relative tilting modules have …