Subring of $\mathbb C$ generated by $\mathbb Z$ and $i$.
Notes: Also isomorphic to $\mathbb Z[x]/(x^2+1)$.
Keywords quotient ring subring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| global dimension | left: 1 | right: 1 |
| Krull dimension (classical) | 1 | |
| 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 | $\{0\}$ |