ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES

Abstract. Let R be a commutative Noetherian ring, and let a and b be two ideals of R such that R=(a + b) is Artinian. Let M and N be two nitely generated R-modules. We prove that Hj b (Hta (M;N)) is Artinian for j = 0; 1, where t = inffi 2 N0 : Hia (M;N) is not nitely generatedg. Also, we prove that if dim Supp (Hia (M;N))  2, then H1 b (Hia (M;N)) is Artinian for all i. More- over, we show that if dimN = d, then Hj b (Hd??1 a (N)) is Artinian for all j  1.