Twisted polynomials $k[x;\sigma]$ for a countable division ring $k$ with endomorphism $\sigma$ which isn't an automorphism. The twist is given by $xa=\sigma(a)x$.

Keywords twisted (skew) polynomial ring

- T.-Y. Lam. A first course in noncommutative rings. (2013) @ p 21

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: $\infty$ |

global dimension | left: 1 | right: |

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

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

Left singular ideal | $\{0\}$ |

Left socle | $\{0\}$ |

Nilpotents | $\{0\}$ |

Right singular ideal | $\{0\}$ |

Right socle | $\{0\}$ |

Zero divisors | $\{0\}$ |