Finiteness properties of generalized local cohomology modules

Let $R$ be a commutative Noetherian ring, $I$ be an ideal of $R$ and $M$ be a finitely generated $R$-module. In this paper, we introduce the concept of $I$,$M$-minimax $R$-modules, and it is shown that if $N$ is an $I$,$M$-minimax $R$-module and $t$ a non-negative integer such that $H^i_I(N)$ is $I$,$M$-minimax for all $i t$, then for all $I$,$M$-minimax submodule $K$ of $H^t_I(M,N)$ the $R$-module $\Hom_R(R/I, H^t_I(M,N)/K)$ is $I$,$M$-minimax. As consequence, it is shown that $\Ass_R H^t_I(M,N)/K$ is a finite set.