$R=\mathbb Z[X]/(X^2,8)$. Or, if $S=\mathbb Z/8\mathbb Z$, it is also the trivial extension ring $R=T(S, S)$; or also $R=S[X]/(X^2)$

- M. B. Rege, S. Chhawchharia, and others. Armendariz rings. (1997) @ Example 3.2 p 16

Known Properties

Legend

- = has the property
- = does not have the property
- = information not in database

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 | $\{[[0,0],[0,0]],[[0,4],[0,0]]\}$ |