Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First, second, and third change of rings theorems for the Gorenstein
  homological dimensions   Motivated by their impact on homological algebra, the change of rings results
have been the subject of several interesting works in Gorenstein homological
algebra over Noetherian rings.
  In this paper, we investigate the change of rings theorems for the Gorenstein
dimensions over arbitrary rings. Namely, by the use of the notion of strongly
Gorenstein modules, we extend the well-known first, second, and third change of
rings theorems for the classical projective and injective dimensions to the
Gorenstein projective and injective dimensions, respectively. Each of the
results established, in this paper, for the Gorenstein projective dimension is
a generalization of a result established over Noetherian rings and for finitely
generated modules. In this paper, we investigate the change of rings theorems
for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the
notion of strongly Gorenstein modules, we extend the well-known first, second,
and third change of rings theorems for the classical projective and injective
dimensions to the Gorenstein projective and injective dimensions, respectively.
Each of the results established in this paper for the Gorenstein projective
dimension is a generalization of a $G$-dimension of a finitely generated module
$M$ over a noetherian ring $R$.

30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int