Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Behavior of the Auslander condition with respect to regradings   We show that a noetherian ring graded by an abelian group of finite rank
satisfies the Auslander condition if and only if it satisfies the graded
Auslander condition. In addition, we also study the injective dimension, the
global dimension and the Cohen-Macaulay property from the same perspective of
that for the Auslander condtion. A key step of our approach is to establish
homological relations between a graded ring $R$, its quotient ring modulo the
ideal $\hbar R$ and its localization ring with respect to the Ore set $\{\,
\hbar^i\, \}_{i\geq0}$, where $\hbar$ is a homogeneous regular normal
non-invertible element of $R$.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: stat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph