Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Adjoining a universal inner inverse to a ring element
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin