The subring of $\mathbb H$ generated by the $\mathbb Q$-span of $1$, $i$, $j$, and $k$.
| Name | Measure | |
|---|---|---|
| global dimension | left: 0 | right: 0 |
| Krull dimension (classical) | 0 | |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $R$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $R$ |
| Units | $R\setminus\{0\}$ |
| Zero divisors | $\{0\}$ |