Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A "quite superfluous" characterisation of the Jacobson radical of an
  associative ring
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph