Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On square-free and radical factorizations and existence of some divisors   We discuss various square-free and radical factorizations and existence of
some divisors in monoids in the context of: atomicity, ascending chain
condition for principal ideals, a pre-Schreier property, a greatest common
divisor property and a greatest common divisor for sets property.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc