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 …

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 …

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 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 …

Let A/S be a ring extension with S commutative. We prove that ω⊗ S AA is a generalized
tilting module if ωS is a generalized tilting module. In this case, we obtain that⊥ ω-resol …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

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 provide a complete classification of all tilting modules and tilting classes over almost
perfect domains, which generalizes the classifications of tilting modules and tilting classes …

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 …

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 …