RT journal article
T1 Regular ring properties Degraded through inverse limits
A1 Ara, Pere
A1 Goodearl, Ken
A1 O'Meara, Kevin
A1 Pardo Espino, Enrique
A1 Perera, Francesc
A2 Matemáticas
K1 exchange rings
K1 inverse limit
K1 regular rings
K1 refinement
K1 separativity
AB 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. This raises the possibility of using inverse limits to answer the long standing Separativity Problem (in the negative).
PB Repositorio arXiv
YR 2024
FD 2024-05-14
LK http://hdl.handle.net/10498/32200
UL http://hdl.handle.net/10498/32200
LA eng
NO Pere Ara and Francesc Perera were partially supported by the Spanish State Research Agency (grant No. PID2020- 113047GB-I00/AEI/10.13039/501100011033), by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya (grant No. 2017-SGR-1725) and by the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The research of Ken Goodearl was partially supported by US National Science Foundation grant DMS 1601184. Kevin O’Meara thanks the Mathematics Departments of the University of California, Santa Barbara (USA), and of both the Universitat Autònoma de Barcelona and Universidad de Cádiz (Spain) for their hospitality during the early part of our project. Enrique Pardo was partially supported by PAI III grant FQM-298 of the Junta de Andalucía, by the DGI-MINECO and European Regional Development Fund, jointly, through grant PID2020-113047GB-I00, and by the grant “Operator Theory: an interdisciplinary approach”, reference ProyExcel 00780, a project financed in the 2021 call for Grants for Excellence Projects, under a competitive bidding regime, aimed at entities qualified as Agents of the Andalusian Knowledge System, in the scope of the Plan Andaluz de Investigación, Desarrollo e Innovación (PAIDI 2020), Consejería de Universidad, Investigación e Innovación of the Junta de Andalucía.
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026