Let $ T=(A, M, 0, B) $ be a triangular matrix algebra with its corner algebras $ A $ and $ B $
Artinian and $ _AM_B $ an $ A $-$ B $-bimodule. The 2-recollement structures for …

The derived category $ D ({\rm Mod} A) $ of a Gorenstein triangular matrix algebra $ A $
admits an unbounded ladder; and this ladder restricts to $ D^-({\rm Mod}) ${\rm (} resp. $ D …

Let R be an Artin algebra and e be an idempotent of R. Assume that Tor i eRe (Re, G)= 0 for
any G∈ Gproj eRe and i sufficiently large. Necessary and sufficient conditions are given for …

Let $ B\subseteq A $ be an extension of finite dimensional algebras. We provide a sufficient
condition for the existence of triangle equivalences of singularity categories (resp …

We apply the technique of recollement to study the Gorenstein defect categories of triangular
matrix algebras. First, we construct a left recollement of Gorenstein defect categories for a …

In the paper, we investigate the lifting of recollements with respect to Gorenstein-projective
modules. Specifically, a homological ring epimorphism can induce a lifting of the …

In this paper, we consider the singularity category $ D_ {sg}(\mod A) $ and the $\mathbb {Z}
$-graded singularity category $ D_ {sg}(\mod^{\mathbb Z} A) $ for a Gorenstein monomial …

Abstract Let T=(RM 0 S) be a triangular matrix ring with R and S rings and RMS an R–S-
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result …

Abstract Let Λ= A 0 MB be an Artin algebra and BMA a BA-bimodule. We prove that there is
a triangle equivalence D sg (Λ)≅ D sg (A)∐ D sg (B) between the corresponding singularity …

The aim of this paper is to introduce Gorenstein singularity category D gpsgb (A), as the
Verdier quotient of the Gorenstein derived category D gpb (A) by the triangulated …