Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the finiteness of the Gorenstein dimension for Artin algebras   In \cite{SSZ}, the authors proved that an Artin algebra $A$ with infinite
global dimension has an indecomposable module with infinite projective and
infinite injective dimension, giving a new characterisation of algebras with
finite global dimension. We prove in this article that an Artin algebra $A$
that is not Gorenstein has an indecomposable $A$-module with infinite
Gorenstein projective dimension and infinite Gorenstein injective dimension,
which gives a new characterisation of algebras with finite Gorenstein
dimension. We show that this gives a proper generalisation of the result in
\cite{SSZ} for Artin algebras.

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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph