Let $s$ be a field endomorphism from a countably infinite field $k$ to $k$ such that the image $L$ has infinite index in $k$. Define multiplication on $R=k\times k$ by $(x,y)(x',y')=(xx',s(x)y'+yx')$. $R$ is the ring

Keywords triangular ring

- T.-Y. Lam. A first course in noncommutative rings. (2013) @ p 139

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

cardinality | $\aleph_0$ | |

composition length | left: $\infty$ | right: |

Krull dimension (classical) | 0 |

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

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