مشخصات پژوهش

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