Reference(s):

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Metaproperties:

This property has the following metaproperties

• passes to subrings
• passes to the center

This property does not have the following metaproperties

• passes to quotient rings (Counterexample: $R_{ 49 }$ is a homomorphic image of $R_{ 27 }$)
• stable under finite products (Counterexample: $R_{ 9 }$)
• stable under products (counterexample needed)
• forms an equational class (counterexample needed)
• Morita invariant (Counterexample: $R_{ 12 }$ is Morita equivalent to $R_{ 2 }$)
• passes to matrix rings (Counterexample: $R_{ 12 }$ is a matrix ring of $R_{ 2 }$)