Description: Group ring of the quaternion group $\mathcal Q_8$ with the field of two elements $F_2$.

Keywords group ring

Reference(s):

- G. Marks. Reversible and symmetric rings. (2002) @ (page needed)

Symmetric properties

Asymmetric properties

Legend

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

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

cardinality | 256 | |

Krull dimension (classical) | 0 |

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

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

Jacobson radical | Elements of "even weight" |

Left socle | $\{0, \sum_{g\in \mathcal Q_8}g\}$ |

Nilpotents | Elements of "even weight" |

Right socle | $\{0, \sum_{g\in \mathcal Q_8}g\}$ |

Unique maximal ideal | Elements of "even weight" |

Units | elements of "odd weight" |

Zero divisors | Elements of "even weight" |