Reference(s):

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Metaproperties:

This property has the following metaproperties

• passes to localizations
• passes to polynomial rings

This property does not have the following metaproperties

• is local (Counterexample: $R_{ 77 }$)
• passes to $I$-adic completions (Counterexample: $R_{ 92 }$)
• passes to power series ring (Counterexample: $R_{ 132 }$)
• passes to subrings (Counterexample: $R_{ 77 }$ is a subring of $R_{ 4 }$)
• 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)
• passes to matrix rings (Counterexample: $R_{ 187 }$ is a matrix ring of $R_{ 186 }$)
• Morita invariant (Counterexample: $R_{ 187 }$ is Morita equivalent to $R_{ 186 }$)