Local-Global Principle for the Artinianness of Local Cohomology Modules.

Let R be a commutative Noetherian ring, I a proper ideal of R, and M a finitely generated R-module. We prove that there is a local-global principle for the Artinianness of the local cohomology module , i.e., for any integer n > 0, is Artinian for all i < n if and only if is Artinian for all i < n and all prime ideals 𝔭, which deduces one interesting property of filter depth. [ABSTRACT FROM PUBLISHER]