Regular Ring Properties Degraded Through Inverse Limits
Rings and Algebras
2024-11-21 v2
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).
Cite
@article{arxiv.2405.06837,
title = {Regular Ring Properties Degraded Through Inverse Limits},
author = {Pere Ara and Ken Goodearl and Kevin C. O'Meara and Enrique Pardo and Francesc Perera},
journal= {arXiv preprint arXiv:2405.06837},
year = {2024}
}
Comments
Accepted for publication in Journal of Algebra. Minor edits + new section, developing a surjective inverse limit $Q = \varprojlim Q_i$ of regular rings such that $V(Q)$ is not isomorphic to $\varprojlim V(Q_i)$