Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The skew-growth function on the monoid of square matrices   We develop an elementary theory of divisibility on the monoid $M(n,R)^\times$
consisting of all square matrices of size $n\ge 1$ of non-zero determinants
with coefficients in a principal ideal domain $R$. In particular, we show that
any finite subset of the monoid has the least left common multiple up to a
right unit factor. When $R$ is residue finite, we consider a signed generating
series, called the skew growth function, of least common multiples of finite
right equivalence classes of irreducible elements. As an elementary application
of the divisibility theory, we show that the skew-growth function decomposes
into Euler products.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol