Description: For a countably infinite field $k$, the quotient polynomial ring $k[x^{1/2},x^{1/4},x^{1/8},...]/(x)$

Notes: Local with an idempotent, nilpotent maximal ideal.

Keywords polynomial ring quotient 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: $\infty$ |

Krull dimension (classical) | 0 |

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

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