In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative
rings. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. We give support to the …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

Let R be a ring. An R-module N is called Gorenstein cotorsion module if Ext R 1 (F, N)= 0 for
any Gorenstein flat R-module F. We investigate some properties of Gorenstein cotorsion …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.
We show this dimension has nice properties when the ring is coherent, and extend the well …

In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often
infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring …

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary
ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …