Description: Let $F_2$ be the field of two elements, and consider the subring of matrices of the form $\begin{bmatrix}a&b&p&0&0&0\\c&d&q&0&0&0\\0&0&r&0&0&0\\0&0&0&r&s&t\\0&0&0&0&a&b\\0&0&0&0&c&d\end{bmatrix}$ with entries in $F_2$.

Notes: Jacobson radical is the subset with $a=b=c=d=r=0$.

Keywords matrix ring subring

Reference(s):

- T. Nakayama. On Frobeniusean algebras. I. (1939) @ pp 61-633
- T.-Y. Lam. Lectures on modules and rings. (2012) @ Example 16.19(5) p 429

Symmetric properties

Asymmetric properties

Legend

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

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

cardinality | 512 | |

Krull dimension (classical) | 0 |

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

Jacobson radical | The elements with $a=b=c=d=r=0$. |