Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace Ideals and the Gorenstein Property   Let R be a local Noetherian commutative ring. We prove that R is an Artinian
Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss
when the trace ideal of a module coincides with its double annihilator.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-fin