Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein homological dimensions and Auslander categories   In this paper, we study Gorenstein injective, projective, and flat modules
over a Noetherian ring $R$. For an $R$-module $M$, we denote by ${\rm Gpd}_RM$
and ${\rm Gfd}_R M$ the Gorenstein projective and flat dimensions of $M$,
respectively. We show that ${\rm Gpd}_RM<\infty$ if and only if ${\rm
Gfd}_RM<\infty$ provided the Krull dimension of $R$ is finite. Moreover, in the
case that $R$ is local, we correspond to a dualizing complex ${\bf D}$ of
$\hat{R}$, the classes $A'(R)$ and $B'(R)$ of $R$-modules. For a module $M$
over a local ring $R$, we show that $M\in A'(R)$ if and only if ${\rm
Gpd}_RM<\infty$ or equivalently ${\rm Gfd}_RM<\infty$. In dual situation by
using the class $B'(R)$, we provide a characterization of Gorenstein injective
modules.

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The categories of this paper are: dg-ga
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th