On the Properties of Formal Local Cohomology Modules

Let  $(R,m)$ be a commutative Noetherian local ring, $a$ an ideal of $R$. Let $t\in\Bbb N_0$ be an integer and $M$ a finitely generated $R$-module such that the $R$-module $\mathfrak{F}^i_{\mathfrak{a}}(M)$ is $\mathfrak{a}$-cominimax for all $i t$. We prove that For all minimax submodules $N$ of $\mathfrak{F}^i_{\mathfrak{a}}(M)$, the $R$-modules \[ Hom_R(R/\mathfrak{a},\mathfrak{F}^t_{\mathfrak{a}}(M)/N)\hspace{5mm} and \hspace{5mm}Ext^1_R(R/\mathfrak{a},\mathfrak{F}^t_{\mathfrak{a}}(M)/N) \]  are minimax. In particular, the set $Ass_R(\mathfrak{F}^t_{\mathfrak{a}}(M)/N)$ is finite.