47 citations · 84 across the 10 of their papers we have counts for
16 papers
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…
Pure C*-algebras
Ramon Antoine, Francesc Perera, Hannes Thiel +1
We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simp…
The Cuntz semigroup of a ring
Ramon Antoine, Pere Ara, Joan Bosa +2
For any ring , we introduce an invariant in the form of a partially ordered abelian semigroup built from an equivalence relation on the class of countably genera…
Traces on ultrapowers of C*-algebras
Ramon Antoine, Francesc Perera, Leonel Robert +1
Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density o…
Edwards' condition for quasitraces on C*-algebras
Ramon Antoine, Francesc Perera, Leonel Robert +1
We prove that Cuntz semigroups of C*-algebras satisfy Edwards' condition with respect to every quasitrace. This condition is a key ingredient in the study of the realization proble…
Cuntz semigroups of ultraproduct C*-algebras
Ramon Antoine, Francesc Perera, Hannes Thiel
We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semig…