See https://stacks.math.columbia.edu/tag/02JE, or https://stacks.math.columbia.edu/download/examples.pdf#nameddest=02JE
| 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 | $\{0\}$ |