On the set of associated primes of a local cohomology module

Assume R is a local Cohen-Macaulay ring. It is shown that Ass(R)(H-I(l)(R)) is finite for any ideal I and any integer I provided Ass(R)(H-(x, y)(2)(R)) is finite for any x, y is an element of R and Ass(R)(H-(x1,x2,y)(3)(R)) is finite for any y is an element of R and any regular sequence x,, x(2) is an element of R. Furthermore it is shown that Ass,(H-I(l)(R)) is always finite if dim(R) less than or equal to 3. The same statement is even true for dim(R) less than or equal to 4 if R is almost factorial. (C) 2001 Academic Press.