On the finiteness properties of UiAssRExtrn (R/αi,M)

Let alpha be an ideal of a commutative Noetherian local ring R and let M be a finitely generated R-module. Let n be a positive integer such that the support of local cohomology module H-alpha(i)(M) is finite for all i < n. In this note we show that the set ((i is an element of N)Ass(R)Ext(R)(n)(R/alpha(i),M))boolean AND{p is an element of Spec(R):dim R/p > 1} is finite. Also we determine precisely the associated prime ideals p of H-alpha(n)(M) satisfying dimR/p > 1.