Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable range one for rings with central units   The purpose of this paper is to give a partial positive answer to a question
raised by Khurana et al. as to whether a ring $R$ with stable range one and
central units is commutative. We show that this is the case under any of the
following additional conditions: $R$ is semiprime or $R$ is one-sided
Noetherian or $R$ has unit-stable range $1$ or $R$ has classical Krull
dimension $0$ or $R$ is an algebra over a field $K$ such that $K$ is
uncountable and $R$ has only countably many primitive ideals or $R$ is affine
and either $K$ has characteristic $0$ or has infinite transcendental degree
over its prime subfield or is algebraically closed. However, the general
question remains open.

4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph