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Let be an ideal of a commutative Noetherian ring and be a nonnegative integer. Let and be two finitely generated -modules. In certain cases, we give some bounds under inclusion for the annihilators of and in terms of minimal primary decomposition of the zero submodule of , 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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