Let $k$ be a field of characteristic $2$, and $\lambda\in k$ be a (nonzero) element that isn't a root of unity. $R=k\langle x, x^{-1}, y, y^{-1}\rangle/\langle xy-\lambda yx\rangle$.

Keywords free algebra quotient ring twisted group ring

- A. Zalesskii and O. Neroslavskii. There exist simple Noetherian rings with zero divisors but without idempotents. (1977) @ (main result)
- M. Lorenz. K0 of skew group rings and simple noetherian rings without idempotents. (1985) @ Example 1.8 p 46

Symmetric properties

Asymmetric properties

Legend

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

(Nothing was retrieved.)

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

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

Jacobson radical | $\{0\}$ |

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

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