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We show that the first non-finitely generated generalized local cohomology modules $H_{{\frak a}}^i (M,N)$ of a finite modules $M$ and $N$ over a Noetherian ring $R$ with respect to an ideal $\frak{a}$ of $R$ has only finitely many associated primes. This generalizes the corresponding result which is shown in [1] for standard local cohomology module.
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