3 papers
math.RA2026
The Cuntz semigroup of rings with stable rank one
Pere Ara, Francesc Perera, Guillem Quingles
We study the Cuntz semigroup of arbitrary rings with stable rank one. We prove that Cuntz subequivalence between countably generated projective right modules , is equivalent…
math.RA2024
Ideals, quotients, and continuity of the Cuntz semigroup for rings
Ramon Antoine, Pere Ara, Joan Bosa +2
In this paper we explore which part of the ideal lattice of a general ring is parametrized by its Cuntz semigroup and its ambient semigroup . We identify thes…
math.OA2024
The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups
Joan Bosa, Francesc Perera, Jianchao Wu +1
We develop a theory of general quotients for W- and Cu-semigroups beyond the case of quotients by ideals. To this end, we introduce the notion of a normal pair, which allows us to…