Let $V=\oplus_{i\in \mathbb N}\mathbb Q$, and $S=\{(b,b,\ldots)\mid b\in\mathbb Z_{(2)}\}$. The ring $R$ is the subring of $\prod_{i\in \mathbb N}\mathbb Q$ generated by $V$ and $S$.
Keywords direct product localization subring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\oplus Q$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\oplus Q$ |