The construction is a skew polynomial ring $E[t, \rho,\delta]$ where $E$ is a field of characteristic $0$, $\rho$ is a monomorphism $E\to E$, and $\delta$ is a $\rho$-derivation of $E$, that is, an additive map that also satisfies $\delta(ab)=\rho(a)\delta(b)+\delta(a)b$. The set of polynomials $E[t]$ is given a new multiplication that satisfies $ta=\rho(a)t+\delta(a)$. (Specifics about $E$, $\rho$ and $\delta$ to follow.)
Keywords twisted (skew) polynomial ring
| Name | Measure | |
|---|---|---|
| global dimension | left: 1 | right: |
| 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 | $\{0\}$ |