Description: Let $F_2$ be the field of two elements, and $R$ be the subring of matrices in $M_4(F_2)$ of the form $\begin{bmatrix} a&0&b&c\\ 0&a&0&d\\ 0&0&a&0\\ 0&0&0&e\end{bmatrix}$

Notes: The field does not have to be finite for the asymmetry of Kasch property: it can be any division ring.

Keywords matrix ring subring

Reference(s):

- T.-Y. Lam. Lectures on modules and rings. (2012) @ p 281

Symmetric properties

Asymmetric properties

Legend

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

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

cardinality | 32 | |

composition length | left: 6 | right: 6 |

Krull dimension (classical) | 0 |

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