Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Some Counterexamples in Ring Theory
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th