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
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |