If $A$ is a ring and $Z(A)$ is its center then what is a sufficient condition for the projective dimension of $A$ over $Z(A)$ (ie: $pd_{Z(A)}(A)$) to be finite?
(Assuming that $A\neq Z(A)$).
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1$\begingroup$ The silly answer: A being commutative. $\endgroup$– Fernando MuroCommented Jan 4, 2015 at 14:59
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$\begingroup$ What if we assume $Z(A)\neq A$? $\endgroup$– ABIMCommented Jan 4, 2015 at 15:02
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$\begingroup$ @CSA: You could ask that $Z(A)$ has finite global dimension. Perhaps explaining what example you have in mind may help us to give you a more useful sufficient condition. $\endgroup$– user91132Commented Dec 25, 2015 at 22:53
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