Year: 2026
Type: preprint
Abstract: We study the Cuntz semigroup of arbitrary rings with stable rank one. We prove that Cuntz subequivalence between countably generated projective right modules $P$, $Q$ is equivalent to $P$ being isomorphic to a pure submodule of $Q$, whilst Cuntz equivalence amounts to isomorphism.~We also prove order-cancellation of finitely generated projective modules (and, more generally, pairs of modules admitting certain complements) from direct sums with countably generated projective modules.
Source: arXiv (Cornell University)
Authors: Ara, Pere, Perera, Francesc, Quingles, Guillem
Institution: Universitat Autònoma de Barcelona
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213257516