Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent Elements of Vertex Algebras   Using the method of commutative algebra, we show that the set $\mathfrak{R}$
of nilpotent elements of a vertex algebra $V$ forms an ideal, and
$V/\mathfrak{R}$ has no nonzero nilpotent elements.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int