A note on injective dimension of local cohomology modules

Abstract

In this study, we assume that R is a commutative Noetherian ring with nonzero identity. We present upper bounds for the injective dimension of I, where I is any ideal in the ring R, in terms of the injective dimension of its local cohomology modules and an upper bound for the injective dimension that involves the theory of local cohomology modules. Since I is an ideal in R, we obtain applications of the theory in a general context.