Some bounds for the annihilators of local cohomology and Ext modules

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.