Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on isomorphisms between submonoids of $\mathbb N^k$ and numerical
  semigroups   Given a submonoid $H$ of $\mathbb N^k$, we give some characterizations of the
minimum $r\in \mathbb N^+$ such that $H$ is isomorphic to a submonoid of
$\mathbb N^r$. In the context of submonoids of $\mathbb N$, we prove that if
two numerical semigroups are isomorphic submonoids of $\mathbb N$, then they
are equal and the identity map is the unique isomorphism between them.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom