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

- W. Nicholson and M. Yousif. On perfect simple-injective rings. (1997) @ Example 2 p 983

Symmetric properties

Asymmetric properties

Legend

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

(Nothing was retrieved.)

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Right socle | $\{0\}$ |