Andreas Thom

Commutators in Continuous Regular Rings

Let $R$ be a continuous von Neumann regular ring with no nonzero abelian idempotents. We prove that every element of $R$ is a single additive commutator. In particular, every operator affiliated with a type $\mathrm{II}_1$ von Neumann algebra is a commutator of operators affiliated with the same algebra. Our commutator...