$R = \begin{bmatrix}\Bbb Z & \Bbb Z/(2) & \Bbb Z & \Bbb Z/(2) \\ 0 & \Bbb Z/(2) & 0 & \Bbb Z/(2) \\ 0 & 0 & \Bbb Z & 0 \\ 0 & 0 & 0 & \Bbb Z/(2) \end{bmatrix}$
Keywords matrix ring triangular ring
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Jacobson radical | Subset of strictly upper triangular matrices |
| Left socle | $\begin{bmatrix}0 & \Bbb Z/(2) & 0 & \Bbb Z/(2) \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}$ |
| Nilpotents | Subset of strictly upper triangular matrices |
| prime radical | Subset of strictly upper triangular matrices |
| Right socle | $ \begin{bmatrix}0 & 0 & 0 & \Bbb Z/(2) \\ 0 & 0 & 0 & \Bbb Z/(2) \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & \Bbb Z/(2) \end{bmatrix}$ |