The center $ Z (\mathcal {A}) $ of an abelian category $\mathcal {A} $ is the endomorphism
ring of the identity functor on that category. A localizing subcategory of a Grothendieck …

For a self-orthogonal module T, the relation between the quotient triangulated category D b
(A)/K b (add T) and the stable category of the Frobenius category of T-Cohen-Macaulay …

Let R be a commutative noetherian local ring. As an analog of the notion of the dimension of
a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of …

We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules
over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order …

The aim of this paper is twofold. On one hand, we prove a slight generalization of the
stability for Gorenstein categories in [SWSW] and [Huang]; and show that the relative …

Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …

We show that the quotient of a Hom‐finite triangulated category 𝒷 by the kernel of the functor
Hom𝒷 (T,−), where T is a rigid object, is preabelian. We further show that the class of regular …

We study certain Schur functors which preserve singularity categories of rings and we apply
them to study the singularity category of triangular matrix rings. In particular, combining …

In this paper we are interested in studying the stability question of subcategories of an
abelian category 𝒜 A constituted of all objects that admit (proper) coproper resolutions …

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …