Reference(s):

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Metaproperties:

This property has the following metaproperties

• passes to quotient rings

This property does not have the following metaproperties

• passes to subrings (Counterexample: $R_{ 1 }$ is a subring of $R_{ 2 }$)
• stable under finite products (Counterexample: $R_{ 9 }$)
• stable under products (counterexample needed)
• forms an equational class (counterexample needed)
• passes to polynomial rings (Counterexample: $R_{ 7 }$ is the polynomial ring of $R_{ 2 }$)
• passes to matrix rings (Counterexample: $R_{ 12 }$ is a matrix ring of $R_{ 2 }$)
• Morita invariant (Counterexample: $R_{ 12 }$ is Morita equivalent to $R_{ 2 }$)