The polynomial ring $\mathbb Z[x]$ over the integers.
Notes: All prime ideals are $1$-or-$2$ generated, but $(3,x,y)$ is not.
Keywords polynomial ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | 2 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Units | $\{-1,1\}$ |
| Zero divisors | $\{0\}$ |