The ring direct product of infinitely many copies of the field of two elements

Notes: By Cantor's diagonal argument, the ring is uncountable.

Keywords direct product

Known Properties

Legend

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

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

cardinality | $\mathfrak c$ | |

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

Krull dimension (classical) | 0 | |

weak global dimension | 0 |

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

Jacobson radical | $\{0\}$ |

Left singular ideal | $\{0\}$ |

Nilpotents | $\{0\}$ |

Right singular ideal | $\{0\}$ |