We study the $ t $-structure induced by an $ n $-tilting module $ T $ in the derived category
$\mathcal {D}(R) $ of a ring $ R $. Our main objective is to determine when the heart of the …

We introduce the notion of big tilting complexes over associative rings, which is a
simultaneous generalization of good tilting modules and tilting complexes over rings. Given …

An algebra is said to be-tilting finite provided it has only a finite number of-rigid objects up to
isomorphism. To each such algebra, we associate a category whose objects are the wide …

Extriangulated categories give a simultaneous generalization of triangulated categories and
exact categories. In this paper, we study silting subcategories of an extriangulated category …

In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of
an abelian length category using torsion classes. To each interval [U, T] in the lattice of …

Let TR be a 1-tilting module with tilting torsion pair (Gen T, F) in Mod-R. The following
conditions are proved to be equivalent:(1) T is pure projective;(2) Gen T is a definable …

For four wide classes of topological rings R, we show that all flat left R-contramodules have
projective covers if and only if all flat left R-contramodules are projective if and only if all left …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …

Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …

D. Happel, I. Reiten and S. Smalø initiated an investigation of quasitilted artin $ K $-algebras
that are the endomorphism rings of tilting objects in hereditary abelian categories whose …