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math.RA2026
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…
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.RA2024
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.…