Let R be a commutative noetherian local ring and consider the set of isomorphism classes of
indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it …

We introduce the notion of ω-Gorenstein modules, where ω is a faithfully balanced self-
orthogonal module. This gives a common generalization of both Gorenstein projective …

Let R be a Gorenstein local ring. We show that for a balanced big Cohen–Macaulay module
M over R, the Cousin complex provides a Gorenstein injective resolution of M. Also, over a d …

A complex C is called Gorenstein injective if there exists an exact sequence of
complexes⋯→ I− 1→ I0→ I1→⋯ such that each Ii is injective, C= Ker (I0→ I1) and the …

There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

Duality properties are studied for a Gorenstein algebra that is finite and projective over its
center. Using the homotopy category of injective modules, it is proved that there is a local …

We generalize the homological characterization of sequentially Cohen–Macaulay modules
over a graded Gorenstein algebra to sequentially reflexive modules over Noetherian, not …

Let $ R $ be a two-sided Noetherian ring, and let $ M $ be a nilpotent $ R $-bimodule, which
is finitely generated on both sides. We study Gorenstein homological properties of the tensor …

Let A and B be rings, U a (B, A)-bimodule and T= A 0 UB be a triangular matrix ring. We first
give an explicit description for Gorenstein injective T-modules over the triangular matrix ring …

The notion of an $\mathcal {L} $ complex (for a given class of $ R $-modules $\mathcal {L} $)
was introduced by Gillespie: a complex $ C $ is called $\mathcal {L} $ complex if $ C $ is …