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