A Note on the injective dimension of local cohomology modules
Abstract
For a noetherian ring R we call an R-module M cofinite if there exists an ideal I of R such that M is I-cofinite; we show that every cofinite module M satisfies dimR(M)<=injdimR(M). As an application we study the question which local cohomology modules HiI(R) satisfy injdimR(HiI(R)) = dimR(HiI(R)). There are two situations where the answer is positive. On the other hand we present two counter-examples, the failure in these two examples coming from different reasons.
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