Group ring of the quaternion group $\mathcal Q_8$ with the field of two elements $F_2$.
Keywords group ring
| 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" |