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
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Right socle | $\{0\}$ |