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Abstract
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Let (R,m) be a commutative Noetherian local ring, I an ideal of R and let M be a non-zero
I -cofinite R-module. In this paper we show that if M has finite injective dimension, then
dim R/I inj dim M depth R; and inj dim M = depth R, whenever mM = M. These
generalize the classical Bass formulas for injective dimension. As an application we obtain
some results on the injective dimension of local cohomology modules. In addition, we show
that R is a Cohen–Macaulay ring if admits a Cohen–Macaulay R-module of finite projective
dimension
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