Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …

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 …

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 …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

We introduce the notion of ω-Gorenstein modules, where ω is a faithfully balanced self-
orthogonal module. This gives a common generalization of both Gorenstein projective …

Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …

A new homological symmetry condition is exhibited that extends and unifies several recently
defined and widely used concepts. Applications include general constructions of tilting …

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive
closure of a tilting module. Applications go in three directions. The first is to characterize …

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 introduce and study the notion of Gorenstein silting complexes, which is a generalization
of Gorenstein tilting modules in Gorenstein-derived categories. We give the equivalent …