The Clifford algebra of a $3$ dimensional $\mathbb R$ vector space with bilinear form having signature $(+1,+1,-1)$. This algebra is isomorphic to $M_2(\mathbb R)\times M_2(\mathbb R)$. In addition to being viewed as a "geometric algebra" for the space, it can also be viewed as the "conformal geometric algebra" for a $1$ dimensional real vector space.
Keywords Clifford algebra direct product matrix ring
| Name | Measure | |
|---|---|---|
| composition length | left: 4 | right: 4 |
| global dimension | left: 0 | right: 0 |
| Krull dimension (classical) | 0 | |
| uniform dimension | left: 4 | right: 4 |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $R$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $R$ |