Ring $R_{ 170 }$

Description:

Take $S=R_{72}$ and the idempotent $e=E_{11}+E_{33}+E_{44}+E_{55}$. This turns out to be a full idempotent, and the required ring is the corner ring $R=eSe$. In other words, $R=\begin{bmatrix}a&p&0&0 \\ 0&r&0&0 \\ 0&0&r&s \\ 0&0&0&a\end{bmatrix}$ for $a,p,r,s\in F_2$.

Keywords basic ring matrix ring subring