Definition: (right nonzero socle) Nonzero right socle

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- stable under products
- stable under finite products

- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)
- passes to quotient rings (Counterexample: $R_{ 69 }$ is a homomorphic image of $R_{ 46 }$)

Rings

Legend

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