The direct limit of the matrix rings in the family $M_{2^n}(\mathbb Q)$ where the rings embed in each other as $A\mapsto \begin{bmatrix}A&0\\0&A\end{bmatrix}$
Keywords direct limit infinite matrix ring matrix ring
| Name | Measure | |
|---|---|---|
| global dimension | left: 1 | right: 1 |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |