Description: The ring of integers $\mathbb Z=\{...-3, -2, -1, 0, 1, 2, 3,...\}$ OR equivalence relation on $\mathbb N\times \mathbb N$ given by $(a,b)\sim(c,d)$ iff $a-b=c-d$

Keywords equivalence relation

Reference(s):

- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 20

Known Properties

Legend

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

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

cardinality | $\aleph_0$ | |

composition length | left: $\infty$ | right: $\infty$ |

global dimension | left: 1 | right: 1 |

Krull dimension (classical) | 1 | |

weak global dimension | 1 |

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Jacobson radical | $\{0\}$ |

Nilpotents | $\{0\}$ |

Units | $\{-1, 1\}$ |

Zero divisors | $\{0\}$ |