We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …

Gorenstein derived categories are defined, and the relation with the usual derived
categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of …

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 …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

Let be an Artin algebra. Under suitable conditions, we describe all the modules in⊥ Λ, and
obtain criteria for the Gorensteinness of Λ. As applications, we determine explicitly all the …

Given a finite-dimensional algebra A over a field k, and a finite acyclic quiver Q, let Λ= A⊗ k
kQ, where kQ is the path algebra of Q over k. Then the category Λ-mod of Λ-modules is …

We study Morita rings Λ (ϕ, ψ)= AANBBMAB Λ_(ϕ,ψ)=\left(A&_AN_B\_BM_A&B) in the
context of Artin algebras from various perspectives. First we study covariantly finite …

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 …

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 …