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 …

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

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …

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 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 …

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 …

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 …

We construct new complete cotorsion pairs in the categories of modules and chain
complexes over a Gorenstein ring $ R $, from the notions of Gorenstein homological …