Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On relative commuting probability of finite rings   In this paper we study the probability that the commutator of a randomly
chosen pair of elements, one from a subring of a finite ring and other from the
ring itself equals to a given element of the ring.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th