Let $S=\prod_{i\in \mathbb N}\mathbb R$, and let $T$ be the ideal of sequences of finite support. Select a maximal ideal $M$ of $S$ containing $T$. The hyperreals can be realized as the quotient ring $R=S/T$.

Keywords direct product equivalence relation

- H. J. Keisler. Elementary calculus: An infinitesimal approach. (2012) @ Epilogue

Known Properties

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

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

cardinality | $\mathfrak{c}$ | |

global dimension | left: 0 | right: 0 |

Krull dimension (classical) | 0 | |

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 | $\{0\}$ |