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

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

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 | $R$ |