We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove
that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that …

We investigate the behavior of singularity categories and stable categories of Gorenstein
projective modules along a morphism of rings. The natural context to approach the problem …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

Let $ R $ be a Ding-Chen ring. Yang\cite {Yang2012} and Zhang\cite {Zhang2015} asked
whether or not every $ R $-module has finite Ding projective or Ding injective dimension. In …

In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …

An integral domain R is called a Gorenstein Prüfer (G-Prüfer) domain if it is coherent and
every submodule of a flat R-module is Gorenstein flat. In this paper, we show that every n-FC …

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory CC
of an abelian category AA, and prove that the right Gorenstein subcategory rG (G (C) G (C)) …

It is proved that a module M over a commutative noetherian ring R is injective if Ext _ R^ i
((R/\mathfrak p) _\mathfrak p, M)= 0 Ext R i ((R/p) p, M)= 0 holds for every i\geqslant 1 i⩾ 1 …

The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the
category of totally reflexive modules over R is representation infinite, provided that it …