Let R be a commutative Noetherian ring, I an ideal of R. Let t ∈ N0 be an integer and M an R-module such that Ext iR (R/I, M ) is minimax for all i t + 1. We prove that if HI i (M ) is FD 1 (or weakly Laskerian) for all i < t, then the R-modules HI i (M ) are I-cominimax for all i < t and ExtiR (R/I, HI t (M )) is minimax for i = 0, 1. Let N be a finitely generated R-module. We prove that ExtjR (N, HI i (M )) and TorR j (N, HI i (M )) are I-cominimax for all i and j whenever M is minimax and HI i (M ) is FD 1 (or weakly Laskerian) for all i.
