$R$ is the restricted direct product of $\mathbb R$ and the $p$-adic rings $\mathbb Q_p$. That is, it is the subring of $\mathbb R\times\prod_p \mathbb Q_p$ of elements for which all but finitely many coordinates lie in $\mathbb Z_p$ for each respective position indexed by $p$.

Keywords direct product subring

Known Properties

Legend

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

(Nothing was retrieved.)

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

Jacobson radical | $\{0\}$ |

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

Left socle | $\mathbb R\oplus (\bigoplus \mathbb Q_p)$ |

Nilpotents | $\{0\}$ |

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

Right socle | $\mathbb R\oplus (\bigoplus \mathbb Q_p)$ |