Regular Ring Properties Degraded Through Inverse Limits
Pere Ara, Ken R. Goodearl, K.C. O’Meara, Enrique Pardo, Francesc Perera · arXiv (Cornell University) · 2024
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).