Let $F$ be the algebraic closure of the field of two elements, and $F[t, \sigma]$ be the twisted polynomial ring with $\sigma$ is the automorphism $x\mapsto x^2$ on $F$. Finally, $R$ is the localization $F[t,\sigma]S^{-1}$ where $S$ is the set of nonnegative powers of $t$.
Notes: Has a unique simple right $R$ module (up to isomorphism)
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| global dimension | left: 1 | right: 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |