Recollements of derived module categories are investigated, using a new technique,
ladders of recollements, which are maximal mutation sequences. The position in the ladder …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA …

In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

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 …

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 …

Let $ T=\biggl (\begin {matrix} A&0\\U&B\end {matrix}\biggr) $ be a formal triangular matrix
ring, where $ A $ and $ B $ are rings and $ U $ is a $(B, A) $-bimodule. We prove that:(1) If …

Let S (n) S (n) be the category of invariant subspaces of nilpotent operators with nilpotency
index at most n n. Such submodule categories have been studied already in 1934 by …

In this paper, we obtain necessary and sufficient conditions for all complete projective
resolutions over a Morita ring Δ (0, 0)(A, B, M, N)= AANBBMAB. As special cases, we get a …