Let $S=\mathbb Q[\{x_i\mid i\in\mathbb Z\}]$, and $I$ be the ideal generated by $\{x_zx_{z+a}x_{z+2a}\mid z\in\mathbb Z, a\in \mathbb N^{>0}\}$. The required ring is $R=S/I$, which looks like a polynomial ring in which no monomial contains an arithmetic progression of indices.

Keywords polynomial ring quotient ring

- J. Ram. On the semisimplicity of skew polynomial rings. (1984) @ Example 3.2

Known 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 | $\{0\}$ |

Nilpotents | $\{0\}$ |

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