A note on injective dimension of local cohomology modules

Source 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.Received: 6 March 2025 | Accepted: 10 September 2025