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Keywords:
local cohomology module; Ext module; annihilator; primary decomposition
local cohomology module; Ext module; annihilator; primary decomposition
Summary:
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.
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