The quotient ring $\mathbb Q[x,y]/(x^2-y^3)$ .

Notes: Integral closure is $\mathbb Q[x/y]$.

Keywords polynomial ring quotient ring

- H. C. Hutchins. Examples of commutative rings. (1981) @ Example 14 p 56
- O. Zariski and P. Samuel. Commutative algebra. (1958) @ p 262

Known Properties

Legend

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

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

cardinality | $\aleph_0$ | |

composition length | left: $\infty$ | right: $\infty$ |

Krull dimension (classical) | 1 |

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

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

Jacobson radical | $\{0\}$ |

Left singular ideal | $\{0\}$ |

Left socle | $\{0\}$ |

Nilpotents | $\{0\}$ |

Right singular ideal | $\{0\}$ |

Right socle | $\{0\}$ |

Zero divisors | $\{0\}$ |