The quotient ring $F_2[x,y]/(x,y)^2$ for the field $F_2$ of two elements.

Notes: Lattice of proper ideals is the diamond lattice. All ideals principal except for maximal ideal.

Keywords quotient ring

- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 19 p 58
- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 173 p 144
- R. W. Gilmer. Multiplicative ideal theory. (1972) @ p 43

Known Properties

Legend

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

Name | Measure | |
---|---|---|

cardinality | 8 | |

composition length | left: 3 | right: 3 |

Krull dimension (classical) | 0 |

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Jacobson radical | Elements of "even weight" |

Left singular ideal | Elements of "even weight" |

Left socle | Elements of "even weight" |

Nilpotents | Elements of "even weight" |

Right singular ideal | Elements of "even weight" |

Right socle | Elements of "even weight" |

Unique maximal ideal | Elements of "even weight" |

Units | Elements of "odd weight." |

Zero divisors | Elements of "even weight" |