Definition: (right simple socle) The right socle is a minimal right ideal

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- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)
- 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