On the associated primes of generalized local cohomology modules

Let alpha be an ideal of a commutative Noetherian ring R with identity and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that Ass(R)(H-alpha(t)(M,N)) is contained in the union of sets Ass(R)(Ext(R)(i)(M, H-alpha(t-1) (N))), where 0 <= i <= t. As an immediate consequence, it follows that if either H-alpha(i)(N) is finitely generated for all i < t or Supp(R)(H-alpha(i)(N)) is finite for all i < t, then Ass(R)(H-alpha(t)(M,N)) is finite. Also, we prove that if d = pd(M) and n = dim(N) are finite, then H-alpha(d+n)(M,N) is Artinian. In particular, Ass(R)(H-alpha(d+n)(M,N)) is a finite set consisting of maximal ideals.