6 papers · 1 filter
Super adaptable graphs and the realization problem
Pere Ara, Joan Bosa, Laurent Cantier +2
We introduce and study the family of super adaptable monoids, which includes, among many others, all conical refinement monoids that are either finitely generated, or countable, pr…
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…
Positive definite matrices and involutions: the manners of their infinite cousins
Pere Ara, Ken Goodearl, Kevin C. O'Meara
Matrices and involutions in/on the algebras and of real (resp., complex) row- and column-finite matrices are studied. It is proved that a…
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…
Regular Ring Properties Degraded Through Inverse Limits
Pere Ara, Ken Goodearl, Kevin C. O'Meara +2
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank.…
The separativity problem in terms of varieties and diagonal reduction
Pere Ara, Ken Goodearl, Pace P. Nielsen +2
We provide two new formulations of the separativity problem. First, it is known that separativity (and strong separativity) in von Neumann regular (and exchange) rings is tightly c…