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Let $R$ be a commutative Noetherian local ring with maximal ideal $\mathfrak m$.

Is it true that the projective dimension of $R/\mathfrak m$ is finite knowing that its injective dimension is finite? If yes, why?!?

I would need this to prove something else but I'm not sure I can use it. Can you help me please?

Thanks.

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    Maybe the "global dimension theorem" will help. cf. Weibel... haven't thought about this though, but that's just where I'd look first.2012-03-29

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