Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indecomposable Ideals in Incidence Algebras   The elements of a finite partial order $P$ can be identified with the maximal
indecomposable two-sided ideals of its incidence algebra $\A$, and then for two
such ideals, $I\prec J \iff IJ \not=0$. This offers one way to recover a poset
from its incidence algebra. In the course of proving the above, we classify all
of the two-sided ideals of $\A$.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: stat