Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Generated Normal Domains From Graphs   Determining whether an arbitrary subring $R$ of $k[x_1^{\pm 1},\dots,
x_n^{\pm 1}]$ is a normal domain is, in general, a nontrivial problem, even in
the special case of a monomial generated domain. In this paper, we provide a
complete characterization of the normality and normalizations of
quadratic-monomial generated domains. For a quadratic-monomial generated domain
$R$, we develop a combinatorial structure that assigns, to each quadratic
monomial of the ring, an edge in a mixed signed, directed graph $G$, i.e., a
graph with signed edges and directed edges. We classify the normality and the
normalizations of such rings in terms of a generalization of the combinatorial
odd cycle condition on $G$.

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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat