Triangular ring $\begin{bmatrix}\mathbb Z&\mathbb Q \\ 0&\mathbb Q\end{bmatrix}$.
Keywords triangular ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| global dimension | left: | right: 1 |
| Name | Description |
|---|---|
| Jacobson radical | $\begin{bmatrix}0&\mathbb Q\\0&0\end{bmatrix}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\begin{bmatrix}0&\mathbb Q\\0&\mathbb Q\end{bmatrix}$ |