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.

- K. Goodearl. Simple self-injective rings need not be artinian. (1974) @ Example 1 p 86

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

weak global dimension | 0 |

Name | Description |
---|---|

Jacobson radical | $\{0\}$ |

Left singular ideal | $\{0\}$ |

Right singular ideal | $\{0\}$ |