Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Algebraic Shift Equivalence of Matrices over Polynomial Rings   The paper studies algebraic strong shift equivalence of matrices over
$n$-variable polynomial rings over a principal ideal domain $D$($n\leq 2$). It
is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full
rank factorization and every non-nilpotent matrix over $D[x]$ is algebraically
strong shift equivalent to a nonsingular matrix. In the case $n=2$, an example
of non-nilpotent matrix over $\mathbb{R}[x,y,z]=\mathbb{R}[x][y,z]$, which can
not be algebraically shift equivalent to a nonsingular matrix, is given.

34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int