dc.contributor.author
Ara, P.
dc.contributor.author
Goodearl, K.
dc.contributor.author
O'Meara, K. C.
dc.contributor.author
Pardo, E.
dc.contributor.author
Perera, F.
dc.date.accessioned
2025-01-15T11:20:50Z
dc.date.available
2025-01-15T11:20:50Z
dc.date.issued
2025-02-15
dc.identifier.uri
http://hdl.handle.net/2072/480042
dc.description.abstract
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).
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dc.description.sponsorship
ere 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 Maria 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 Autonoma de Barcelona and Universidad de Cadiz (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 Andalucia, 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 Investigacion, Desarrollo e Innovacion (PAIDI 2020), Consejeria de Universidad, Investigacion e Innovacion of the Junta de Andalucia.
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dc.format.extent
33 p.
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dc.relation.ispartof
Journal of Algebra
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dc.rights
(c) 2024 The Author(s)
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.subject.other
Exchange rings
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dc.subject.other
Inverse limit
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dc.subject.other
Regular rings
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dc.subject.other
Refinement
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dc.subject.other
(Strong) separativity
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dc.title
Regular ring properties degraded through inverse limits
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.jalgebra.2024.11.006
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
