Let $L$ be an irreducible continuous geometry in case $\infty$ (i.e. fails the DCC) as constructed in von Neumann's Examples of Continuous Geometries. The ring resulting from von Neumann's coordinatization theorem is the required ring.
| Name | Measure | |
|---|---|---|
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Right singular ideal | $\{0\}$ |