Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Subrings which are closed with respect to taking the inverse
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph