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 Hi I (N) is I,Mminimax for all i < t, then for all I,M-minimax submodule K of Ht I (M,N) the R-module HomR(R/I,Ht I (M,N)/K) is I,M-minimax. As consequence, it is shown that AssR Ht I (M,N)/K is a finite set.