Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitary stable ranks and norm-one ranks   In the context of commutative $C^*$-algebras we solve a problem related to a
question of M. Rieffel by showing that the all-units rank and the norm-one rank
coincide with the topological stable rank. We also introduce the notion of
unitary $M$-stable rank for an arbitrary commutative unital ring and compare it
with the Bass stable rank. In case of uniform algebras, a sufficient condition
for norm-one reducibility is given.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci