Definition: (right simple-injective) If $T$ is a right ideal of $R$, and $f:T\to R$ such that $f(T)$ is simple, then $f$ can be extended to $R\to R$

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- passes to subrings (Counterexample: $R_{ 14 }$ is a subring of $R_{ 12 }$)
- passes to quotient rings (Counterexample: $R_{ 164 }$ is a homomorphic image of $R_{ 139 }$)

Rings

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