A well-known Assem–Smal ϕ ϕ theorem on tilting modules plays an important role in tilting
theory. In this paper, we prove that a version of Assem–Smal ϕ ϕ theorem still holds in the …

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the
class Cogen M is always a covering class whenever M is a quasi-cotilting module. Some …

Given a noetherian abelian k-category of finite homological dimension, with a tilting object T
of projective dimension 2, the abelian category and the abelian category of modules over …

In this paper, we introduce and investigate Tor-tilting comodules and weak silting
comodules, providing a generalization of the established tilting and silting theories in the …

We study a natural generalization of* n-modules (and hence also of*-modules) by
introducing the notion of*∞-modules. The most important results about* n-modules (and …

In this article, we provide a new generalization of tilting modules, named (generalized) tilting
modules with respect to σ [M], or simply (generalized) M-tilting modules and then …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

The thesis compiles my contributions to the tilting theory, mainly in the set-ting of a module
category over a commutative ring. We give a classification of tilting classes over an arbitrary …

Throughout these notes, k will denote an algebraically closed field and Λ a finite-
dimensional algebra over k. We will denote by mod Λ the category of finite-dimensional right …

Ring epimorphisms often induce silting modules and cosilting modules, termed minimal
silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal …