Some bounds for the annihilators of local cohomology and Ext modules

TL;DR

This paper establishes bounds for the annihilators of local cohomology and Ext modules in Noetherian rings, providing explicit computations in specific cases and advancing understanding of their algebraic structure.

Contribution

It introduces bounds for annihilators of local cohomology and Ext modules that are independent of primary decomposition choices, and applies these bounds to compute annihilators in particular scenarios.

Findings

Derived bounds are independent of primary decomposition.

Computed annihilators explicitly in certain algebraic cases.

Enhanced understanding of the structure of local cohomology and Ext modules.

Abstract

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be a non-negative integer. Let $M$ and $N$ be two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators of $\operatorname{Ext}^t_R(M, N)$ and $\operatorname{H}^t_{\mathfrak a}(M)$ in terms of minimal primary decomposition of the zero submodule of $M$ which are independent of the choice of minimal primary decomposition. Then, by using those bounds, we compute the annihilators of local cohomology and Ext modules in certain cases.