Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A matrix ring with commuting graph of maximal diameter   The commuting graph of a semigroup is the set of non-central elements; the
edges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example of
a field $F$ and an integer $n$ such that the commuting graph of
$\operatorname{Mat}_n(F)$ has maximal possible diameter, equal to six.

34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat