Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Taylor resolution over a skew polynomial ring   Let $\Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring
$Q=\Bbbk[x_1,\ldots,x_n]$. In her thesis, Taylor introduced a complex which
provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda
constructed a differential graded structure on the Taylor resolution. More
recently, Avramov showed that this differential graded algebra admits divided
powers. We generalize each of these results to monomial ideals in a skew
polynomial ring $R$. Under the hypothesis that the skew commuting parameters
defining $R$ are roots of unity, we prove as an application that as $I$ varies
among all ideals generated by a fixed number of monomials of degree at least
two in $R$, there is only a finite number of possibilities for the Poincar\'{e}
series of $\Bbbk$ over $R/I$ and for the isomorphism classes of the homotopy
Lie algebra of $R/I$ in cohomological degree larger or equal to two.

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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio