Let R be a commutative noetherian ring, a an ideal of R and M,N finite R–modules. We prove that the following statements are equivalent. (i) Hi (M,N) is finite for all i < n. (ii) CoassR(Hi (M,N)) ⊂ V(a) for all i < n. (iii) Hi (M,N) is coatomic for all i < n. If pdM is finite and r be a non-negative integer such that r > pdM and Hi (M,N) is finite (resp. minimax) for all i ≥ r, then Hi (M,N) is zero (resp. artinian) for all i ≥ r. Mathematics Subject Classification: 13D45, 13D07
