The ring of all holomorphic functions on the complex numbers
Notes: Not a UFD
Keywords ring of functions
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak c$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | $>=\mathfrak c$ | |
| weak global dimension | 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 | $\{0\}$ |