Abstract
Let $\fa$ be an ideal of a commutative Noetherian ring and a finitely generated -module. Let be a natural integer. It is shown that there is a finite subset of $\Spec R$, such that $\Ass_R(H_{\fa}^t(M))$ is contained in union with the union of the sets $\Ass_R(\Ext_R^j(R/\fa,H_{\fa}^i(M)))$, where and . As an immediate consequence, we deduce that the first non $\fa$-cofinite local cohomology module of with respect to $\fa$ has only finitely many associated prime ideals.
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