With real numbers $\mathbb R$, $\mathbb R[x]/(x^2+1)$ OR the set of real matrices of form $\left[\begin{smallmatrix}a&b\\-b&a\end{smallmatrix}\right]$ OR the real Clifford algebra for signature (-)
Keywords matrix ring quotient ring subring
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak{c}$ | |
| composition length | left: 1 | right: 1 |
| global dimension | left: 0 | right: 0 |
| Krull dimension (classical) | 0 | |
| uniform dimension | left: 1 | right: 1 |
| 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 | $\{0\}$ |