Let R be a commutative Noetherian ring, a an ideal of R and M a finite R–modules. Let X be an arbitrary R–module (not necessary finite) and n be a non- negative integer. It is shown that n n i (i) SuppR (H a (M, X)) ⊆ ∪i=0 Supp R (Ha (X)); (ii) AssR(H a n (M, X)) ⊆ AssR(Ha n (X)) ∪ (∪n−1 i=0 SuppR (Ha i (X))). We also study cominimaxness of generalized local cohomology modules in several cases.
