Definition: Only ideals are the two trivial ideals

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- passes to quotient rings
- Morita invariant
- passes to matrix rings
- passes to $eRe$ for any full idempotent $e$

- passes to polynomial rings (Counterexample: $R_{ 3 }$)
- stable under finite products (Counterexample: $R_{ 9 }$)
- stable under products (counterexample needed)
- forms an equational class (counterexample needed)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)

Rings

Legend

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