Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorizations in bounded hereditary Noetherian prime rings   If $H$ is a monoid and $a=u_1 \cdots u_k \in H$ with atoms (irreducible
elements) $u_1, \ldots, u_k$, then $k$ is a length of $a$, the set of lengths
of $a$ is denoted by $\mathsf L(a)$, and $\mathcal L(H)=\{\,\mathsf L (a) \mid
a \in H \,\}$ is the system of sets of lengths of $H$. Let $R$ be a hereditary
Noetherian prime (HNP) ring. Then every element of the monoid of
non-zero-divisors $R^\bullet$ can be written as a product of atoms. We show
that, if $R$ is bounded and every stably free right $R$-ideal is free, then
there exists a transfer homomorphism from $R^{\bullet}$ to the monoid $B$ of
zero-sum sequences over a subset $G_{\textrm{max}}(R)$ of the ideal class group
$G(R)$. This implies that the systems of sets of lengths, together with further
arithmetical invariants, of the monoids $R^{\bullet}$ and $B$ coincide. It is
well-known that commutative Dedekind domains allow transfer homomorphisms to
monoids of zero-sum sequences, and the arithmetic of the latter has been the
object of much research. Our approach is based on the structure theory of
finitely generated projective modules over HNP rings, as established in the
recent monograph by Levy and Robson. We complement our results by giving an
example of a non-bounded HNP ring in which every stably free right $R$-ideal is
free but which does not allow a transfer homomorphism to a monoid of zero-sum
sequences over any subset of its ideal class group.

1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org