*This ring suggested by: Watson*

Description: Let $k$ be a countably infinite field, $V$ be an infinite dimensional $k$-vector space, and consider the trivial extension $T(k,V)$.

Notes: Radical has square zero.

Keywords trivial extension

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 | $\{0,1\}$ |