The $I$-adic completion of $\mathbb R[x,y]$ where $I=(x^2+y^2-1)$.

Keywords completion polynomial ring

- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 109 p 109
- R. M. Fossum. The divisor class group of a Krull domain. (1973) @ p 113

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) | 2 |

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

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

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

Left socle | $\{0\}$ |

Nilpotents | $\{0\}$ |

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

Right socle | $\{0\}$ |

Zero divisors | $\{0\}$ |