Field of fractions of the integers $\mathbb Z$

Notes: smallest ordered field

Keywords equivalence relation ring of quotients

Known Properties

Legend

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

Name | Measure | |
---|---|---|

cardinality | $\aleph_0$ | |

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 | $\{0\}$ |