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 …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

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 determine all the Gorenstein-projective modules over the T2-extension of a Gorenstein
algebra, and over (AM0B), where A and B are self-injective algebras, and M is an AB …

Inspired by recent results of Ringel–Schmidmeier, Kussin–Lenzing–Meltzer, Xiao-Wu Chen,
and Pu Zhang, given a field K, m≥ 1, and a finite poset I≡(I,⪯) with a unique maximal …

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

We prove a generalization of the stability for Gorenstein categories in [36] and [24]; and
show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other …

The paper is an addition to our article Simson (2015)[37]. Given a field K, an integer m≥ 1,
and a finite poset I≡(I,⪯) with a unique maximal element⁎, we study the category M on (I, F …