See Nishimura, Jun-Ichi. "A few examples of local rings, I." Kyoto Journal of Mathematics 52.1 (2012): 51-87. page 64
| Name | Measure | |
|---|---|---|
| Krull dimension (classical) | 2 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |