Description: Let $F$ be the field of two elements, and consider a countably infinite direct sum of copies of $F$. This is a countable boolean ring (without unity). The required ring is the subring generated by this subrng of $\prod F$ and the identity of $\prod F$. This is still countable. Alternatively, the ring of "eventually constant" sequences in $\prod F$.

Keywords direct product subring

Reference(s):

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: $\infty$ |

Krull dimension (classical) | 0 | |

weak global dimension | 0 |

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

Jacobson radical | $\{0\}$ |

Nilpotents | $\{0\}$ |