The polynomial ring in countably infinitely many variables over $\mathbb R$.
Notes: Uncountability of the base field is necessary to show it is Hilbert.
Keywords polynomial ring
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak c$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | $\infty$ |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |