Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The global dimension of the algebras of polynomial integro-differential
  operators $\mathbb{I}_n$ and the Jacobian algebras $\mathbb{A}_n$   The aim of the paper is to prove two conjectures that the (left and right)
global dimension of the algebra of polynomial integro-differential operators
$\mathbb{I}_n$ and the Jacobian algebra $\mathbb{A}_n$ is equal to $n$ (over a
field of characteristic zero). An analogue of Hilbert's Syzygy Theorem is
proven for them. The algebras $\mathbb{I}_n$ and $\mathbb{A}_n$ are neither
left nor right Noetherian. Furthermore, they contain infinite direct sums of
nonzero left/right ideals and are not domains. It is proven that the global
dimension of all prime factor algebras of the algebras $\mathbb{I}_n$ and
$\mathbb{A}_n$ is $n$ and the weak global dimension of all the factor algebras
of $\mathbb{I}_n$ and $\mathbb{I}_n$ is $n$.

29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org