On the associated primes of generalized local cohomology modules

Let $\text{fa}$ be an ideal of a commutative Noetherian ring $R$ with identity and let $M$ and $N$ be two finitely generated $R$-modules. Let $t$ be a positive integer. It is shown that ${\text{Ass}}_R(H_{\text{fa}}^t(M,N))$ is contained in the union of the sets ${\text{Ass}}_R({\text{Ext}}_R^i(M,H_{\text{fa}}^{t-i}(N)))$, where $0\le i\le t$. As an immediate consequence, it follows that if either $H_{\text{fa}}^i(N)$ is finitely generated for all $i<t$ or ${\text{Supp}}_R(H_{\text{fa}}^i(N))$ is finite for all $i<t$, then ${\text{Ass}}_R(H_{\text{fa}}^t(M,N))$ is finite. Also, we prove that if $d=\text{pd}(M)$ and $n=\dim (N)$ are finite, then $H_{\text{fa}}^{d+n}(M,N)$ is Artinian. In particular, ${\text{Ass}}_R(H_{\text{fa}}^{d+n}(M,N))$ is a finite set consisting of maximal ideals.