Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: An algorithmic approach to the existence of ideal objects in commutative
  algebra
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg