Regular ring properties degraded through inverse limits

Pere Ara; Ken Goodearl; Kevin C. O'Meara; Enrique Pardo; Francesc Perera

doi:10.1016/j.jalgebra.2024.11.006

Regular ring properties degraded through inverse limits

Pere Ara, Ken Goodearl, Kevin C. O'Meara^*, Enrique Pardo, Francesc Perera

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

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Resum

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).

Idioma original	Anglès
Pàgines (de-a)	365-397
Nombre de pàgines	33
Revista	Journal of Algebra
Volum	664
Número	Part B
DOIs	https://doi.org/10.1016/j.jalgebra.2024.11.006
Estat de la publicació	Publicada - 15 de febr. 2025

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10.1016/j.jalgebra.2024.11.006

https://ddd.uab.cat/record/306371

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title = "Regular ring properties degraded through inverse limits",

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).",

keywords = "(Strong) separativity, Exchange rings, Inverse limit, Refinement, Regular rings",

author = "Pere Ara and Ken Goodearl and O'Meara, {Kevin C.} and Enrique Pardo and Francesc Perera",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2025",

month = feb,

day = "15",

doi = "10.1016/j.jalgebra.2024.11.006",

language = "English",

volume = "664",

pages = "365--397",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "Part B",

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TY - JOUR

T1 - Regular ring properties degraded through inverse limits

AU - Ara, Pere

AU - Goodearl, Ken

AU - O'Meara, Kevin C.

AU - Pardo, Enrique

AU - Perera, Francesc

PY - 2025/2/15

Y1 - 2025/2/15

N2 - 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).

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).

KW - (Strong) separativity

KW - Exchange rings

KW - Inverse limit

KW - Refinement

KW - Regular rings

UR - http://www.scopus.com/inward/record.url?scp=85210293204&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/53269486-b7e7-3b67-b45b-efffdc65a2ff/

UR - https://portalrecerca.uab.cat/en/publications/3100fb70-4ad4-43cf-a022-b34be412d91f

U2 - 10.1016/j.jalgebra.2024.11.006

DO - 10.1016/j.jalgebra.2024.11.006

M3 - Article

AN - SCOPUS:85210293204

SN - 0021-8693

VL - 664

SP - 365

EP - 397

JO - Journal of Algebra

JF - Journal of Algebra

IS - Part B

ER -

Regular ring properties degraded through inverse limits

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