Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Rings involving idempotents, units and nilpotent elements
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess