Let $S$ be the ring of linear transformations of a countable dimensional vector space over a field. This is known to have exactly one nontrivial ideal $M$. The ring is $S/M$
| Name | Measure | |
|---|---|---|
| composition length | left: $\infty$ | right: $\infty$ |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |