Ring $R_{ 125 }$

Description:

Let $S$ be $R_{44}$ . There must exist an ordinal $\beta$ such that $Soc_\beta(S_S)=Soc_{\beta+1}(S_S)\neq S$. The required ring is $R=S/Soc_\beta(S_S)$.

Notes: I've reversed sides from the description in the original paper

Keywords infinite matrix ring quotient ring subring