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I'm wondering about the question, "If we have a finitely presented __, is it necessarily finitely presented with respect to any finite generating set for it?" I know this is true for groups and for R-modules. Does anyone know whether this is true for A-algebras? Commutative A-algebras? Other things people might happen to know about it for?

I'm wondering about the question

"If we have a finitely presented __, is it necessarily finitely presented with respect to any finite generating set for it?"

I know this is true for groups and for $R$-modules. Does anyone know whether this is true for $A$-algebras? Commutative $A$-algebras? Other things people might happen to know about it for?

I'm wondering about the question, "If we have a finitely presented __, is it necessarily finitely presented with respect to any finite generating set for it?" I know this is true for groups and for R-modules. Does anyone know whether this is true for A-algebras? Commutative A-algebras? Other things people might happen to know about it for?

I'm wondering about the question, "If we have a finitely presented __, is it necessarily finitely presented with respect to any finite generating set for it?" I know this is true for groups and for R-modules. Does anyone know whether this is true for A-algebras? Commutative A-algebras? Other things people might happen to know about it for?