Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transversal Intersection and Sum of Polynomial Ideals   In this paper we derive some conditions for transversal intersection of
polynomial ideals. We exhibit some examples. Finally, as an application of the
results proved, we compute the Betti numbers for ideals of the form $I_{1}(XY)
+ J$, where $X$ and $Y$ are matrices and $J$ is the ideal generated by the
$2\times 2$ minors of the matrix consisting of any two rows of $X$.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph