Let $V$ be an infinite dimensional right vector space over $\mathbb Q$. Let $T$ be the ring of linear transformations $V\to V$. Let $S$ be the socle of $T$. The ring $R$ is the subring of $T$ generated by $S$ and the center of $T$.
Keywords infinite matrix ring subring
| Name | Measure | |
|---|---|---|
| composition length | left: $\infty$ | right: $\infty$ |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Right singular ideal | $\{0\}$ |