Artinianness of local cohomology modules

TL;DR

This paper establishes general theorems on when local cohomology modules are artinian, extending previous specific results and providing a broader understanding of their structure in noetherian rings.

Contribution

It introduces uniform theorems that determine the artinianness of local cohomology modules in a general setting, generalizing earlier graded case results.

Findings

Proves uniform criteria for artinianness of local cohomology modules.

Extends previous graded case results to a more general context.

Provides new insights into the structure of local cohomology modules.

Abstract

Let $A$ be a noetherian ring, $\fa$ an ideal of $A$, and $M$ an $A$--module. Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.