Let $k$ be a universal differential field with derivation $D$, and let $R=k[y, D]$ be the differential polynomial ring. (Underlying set and addition operation is the same as $k[y]$, and $ya=ay+D(a)$.)
Notes: Has a unique simple right $R$ module (up to isomorphism)
Keywords differential polynomial ring
| Name | Measure | |
|---|---|---|
| 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 | $\{0\}$ |