$R=\mathbb Z[X]/(X^2,8)$. Or, if $S=\mathbb Z/8\mathbb Z$, it is also the trivial extension ring $R=T(S, S)$; or also $R=S[X]/(X^2)$
| Name | Measure | |
|---|---|---|
| cardinality | 64 | |
| Krull dimension (classical) | 0 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left socle | $\{[[0,0],[0,0]],[[0,4],[0,0]]\}$ |
| Right socle | $\{[[0,0],[0,0]],[[0,4],[0,0]]\}$ |