Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dualizing Complex of a Toric Face Ring II: Non-normal Case   The notion of "toric face rings" generalizes both Stanley-Reisner rings and
affine semigroup rings, and has been studied by Bruns, Romer, et.al. Here, we
will show that, for a toric face ring $R$, the "graded" Matlis dual of a Cech
complex gives a dualizing complex. In the most general setting, $R$ is not a
graded ring in the usual sense. Hence technical argument is required.

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin