Let $\sigma:k\to k$ be a field endomorphism of a countable field $k$ such that $\infty > n=[k:\sigma(k)]>1$. $k[x;\sigma]$ is the twisted polynomial ring where $xa:=\sigma(a)x$ for all $a$ in $k$. The ring is $k[x;\sigma]/(x^2)$.

Notes: Composition length finite but different on both sides

- E. A. Rutter and Jr. Rings with the principal extension property. (1975) @ Example 1, pp 208-209
- W. K. Nicholson and M. F. Yousif. Annihilators and the CS-condition. (1998) @ Example 3.8 p 221

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: 1 | right: $n$ |

Krull dimension (classical) | 0 |

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

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