Description: The polynomial ring $k[x]$ over a countably infinite field $k$

Keywords polynomial ring

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: $\infty$ |

global dimension | left: 1 | right: 1 |

Krull dimension (classical) | 1 | |

weak global dimension | 1 |

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

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

Jacobson radical | $\{0\}$ |

Nilpotents | $\{0\}$ |

Units | $k\setminus\{0\}$ |

Zero divisors | $\{0\}$ |