The subring of $\mathbb H$ generated by the $\mathbb Q$-span of $1$, $i$, $j$, and $k$.

Symmetric properties

Asymmetric properties

Legend

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

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 | $\{0\}$ |