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 …

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 …

In this paper, weak tilting modules are introduced and investigated. We show that all tilting
modules are weak tilting modules, but the converse is not true. We prove that a module is …

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

Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein
cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R …

We introduce the notion of Gorenstein star modules and obtain some properties and a
characterization of them. We mainly give the relationship between n-Gorenstein star …

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 …

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 …

In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we
introduce the notions of strongly WP-Gorenstein, WI-Gorenstein and WF-Gorenstein …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …