Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Products of ideals may not be Golod   We exhibit an example of a product of two proper monomial ideals such that
the residue class ring is not Golod. We also discuss the strongly Golod
property for rational powers of monomial ideals, and introduce some sufficient
conditions for weak Golodness of monomial ideals. Along the way, we ask some
related questions.

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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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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: chao-dyn