Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Jordan-H\"older Theorem for Monoids with Group Action   In this article, we prove an isomorphism theorem for the case of refinement
$\Gamma$-monoids. Based on this we show a version of the well-known
Jordan-H\"older theorem in this framework. The main theorem of this article
states that - as in the case of modules - a monoid $T$ has a
$\Gamma$-composition series if and only if it is both $\Gamma$-Noetherian and
$\Gamma$-Artinian. As in module theory, these two concepts can be defined via
ascending and descending chains respectively.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph