Let R be a commutative Noetherian ring. The aim of this paper is studying the properties of
relative Gorenstein modules with respect to a dualizing module. It is shown that every …

Let C be a semidualizing module for a commutative ring R. In this paper, we study the
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …

Let R be a ring and S an excellent extension of R. In this paper we study the Gorenstein
homological dimensions over R and S. We show that if M is an S-module, then MR is …

In this paper, let R be a commutative ring and C a semidualizing module. We investigate the
(weak) C-Gorenstein global dimension of R and we get a simple formula to compute the C …

Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is proved
that FPD (R)= sup {GPC− pd R (M)| M∈ BC (R) and GPC− pd R (M)<∞}, which is a …

The classes of GC homological modules over commutative ring, where C is a semidualizing
module, extend Holm and J gensen's notions of C-Gorenstein homological modules to the …

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 …

Abstract Let $ A $ and $ B $ be rings, $ U $ a $(B, A) $-bimodule, and $ T=\left (\begin
{smallmatrix} A & 0\\U & B\\\end {smallmatrix}\right) $ the triangular matrix ring. In this paper …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

Over a commutative noetherian ring, we introduce a generalization of Gorenstein projective
and injective modules, which we call, respectively, n-Gorenstein projective and injective …