Regular Ring Properties Degraded Through Inverse Limits

2024/05/10 by Pere Ara, Ara, Pere, K. R. Goodearl +7
Computer Science · Mathematics · #18A30 #20M14 #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 16E50 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 16E20

paper · pdf · doi:10.48550/arxiv.2405.06837

openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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).

Related

• Inverse limits of rings and Multiplier rings
• The separativity problem in terms of varieties and diagonal reduction
• Some topological and combinatorial properties preserved by inverse limits
• Regular elements determined by generalized inverses
• Strongly clean ring elements that are one-sided inverses