Ring $R_{ 41 }$

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