A note on some top local cohomology modules

TL;DR

This paper investigates specific top local cohomology modules, especially $H^{d-1}_{a}(R)$, providing new insights into their properties within Noetherian rings.

Contribution

It offers new information on the structure and properties of top local cohomology modules, focusing on the last non-zero modules in Noetherian rings.

Findings

Insights into the structure of $H^{d-1}_{a}(R)$

Conditions for non-vanishing of top local cohomology modules

Relationships between ideal $a$ and top local cohomology modules

Abstract

Let $\fa$ be an ideal of a $d$-dimensional commutative Noetherian ring $R$. In this paper we give some information on some last non-zero local cohomology modules known as top local cohomology modules in particular, $H^{d-1}_{\fa}(R)$.