Abstract
Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M an R-module. We prove that for a fixed non-negative integer n, the nth local cohomology module is finitely generated if and only if
is 𝔞-cofinite and
. This enables us to establish the Noetherian property of local cohomology modules in several cases. Finally, we obtain a new characterization of the cohomological dimensions.
ACKNOWLEDGMENT
The authors are deeply grateful to the referee for carefully reading of the manuscript and helpful suggestions. Also, we would like to thank the Centre of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad (CEAAS) for the financial support.
Notes
Communicated by A. K. Singh.