Description: The polynomial ring in countably infinitely many variables over $\mathbb R$.

Notes: Uncountability of the base field is necessary to show it is Hilbert.

Keywords polynomial ring

Reference(s):

- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 1 p 50
- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 167 p 139

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) | $\infty$ |

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

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

Nilpotents | $\{0\}$ |

Zero divisors | $\{0\}$ |