Regular ring properties degraded through inverse limits

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URI: http://hdl.handle.net/10498/36065

DOI: 10.1016/J.JALGEBRA.2024.11.006

ISSN: 1090-266X

ISSN: 0021-8693

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Author/s
Ara, Pere; Goodearl, Ken; O'Meara, Kevin C.; Pardo Espino, EnriqueAuthority UCA; Perera, Francesc
Date
2025
Department
Matemáticas
Source
Journal of Algebra - 2025, Vol.664 pp.365-397
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).
Subjects
(Strong) separativity; Exchange rings; Inverse limit; Refinement; Regular rings
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