Direct finiteness of representable regular rings with involution
Rings and Algebras
2025-12-02 v8
Abstract
For von Neumann *-regular rings R of endomorphisms (the involution given by taking adjoints) of inner product spaces we provide a condition on r in R (in terms of action of r on finite dimensional subspaces) for r being a unit. It remains open whether this result can be used to prove direct finiteness of R. This was claimed in earlier versions but no proof was given.
Cite
@article{arxiv.1901.03555,
title = {Direct finiteness of representable regular rings with involution},
author = {Christian Herrmann},
journal= {arXiv preprint arXiv:1901.03555},
year = {2025}
}