Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 265-284, 2022
Some bounds for the annihilators of local cohomology and Ext modules
Ali Fathi
Received October 25, 2020. Published online November 22, 2021.
Abstract: Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be a nonnegative integer. Let $M$ and $N$ be two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators of ${\rm Ext}^t_R(M, N)$ and ${\rm H}^t_{\mathfrak a}(M)$ 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.
Keywords: local cohomology module; Ext module; annihilator; primary decomposition
Affiliations: Ali Fathi, Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran, e-mail: fathi_ali@iauz.ac.ir, alif1387@gmail.com
