Definition: (right CS) "Complements are Summands": Every nonzero right ideal is essential in a direct summand of $R_R$.

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- passes to quotient rings (Counterexample: $R_{ 164 }$ is a homomorphic image of $R_{ 139 }$)
- passes to subrings (Counterexample: $R_{ 24 }$ is a subring of $R_{ 11 }$)

Rings

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